Name: three-phase synchronous motor starting and v-curves
Uploaded: 2023-04-30T06:43:16.000Z
Duration: 11 min 19 s
Channel: JoVE

K12 Standards

south-carolina-college-and-career-ready-science-standards

South Carolina College and Career Ready Science Standards

High School

Physics

motion-and-stability-forces-and-interactions

Motion and Stability: Forces and Interactions

P-PS2-6.

AC Synchronous Machine Characterization

1. 直流测试
<ol>
	<li>在电源输出端短路的情况下，打开低功率直流电源。
	<ol>
		<li>将低功率直流电源的电流限制为 1.8 A。</li>
		<li>关闭电源，并断开短路连接。</li>
	</ol>
	</li>
	<li>将电源输出端连接至同步电机的 1 和 4 端口。
	<ol>
		<li>打开电源，测量直流电压和电流。根据需要调节电压，使电流达到 1.8 A。</li>
		<li>关闭电源，然后对端口 2 和 5 以及端口 3 和 6 重复上述两个步骤。</li>
	</ol>
	</li>
	<li>断开低功率直流电源的连接。</li>
</ol>
2. 同步电机启动
<ol>
	<li>确保三相断开开关、同步电机开关和直流电机开关均处于关闭状态。
	<ol>
		<li>检查可变变压器（VARIAC）是否处于0%位置。</li>
		<li>将可变变压器（VARIAC）连接至三相插座，并连接图1所示的装置。</li>
		<li>请记住设置数字功率计电流探头的1到1000倍率。</li>
	</ol>
	</li>
	<li>检查“启动/运行”开关是否处于“启动”位置。</li>
	<li>打开三相断开开关。</li>
	<li>迅速增加可变变压器（VARIAC）输出，直到数字功率计读数约为115 V。</li>
	<li>测量电枢电流IAC1、电枢电压VAC1、有功功率和功率因数。</li>
	<li>请注意，测量的是相（相线对中性线）电压和a相的相电流，因此功率计上的功率因数测量值正确反映了每相的功率因数。</li>
	<li>测量电机的转矩和转速。</li>
	<li>打开125 V直流电源。确保所有连接均已从电源端子处清除。
	<ol>
		<li>按下电源“启动”按钮，并将电源输出设置为125 V。</li>
	</ol>
	</li>
	<li>将“启动/运行”开关拨至“运行”位置。注意电机声音的变化。随着转子磁场与定子旋转磁场锁定，电机声音变得更加平稳。
	<ol>
		<li>记录电枢电流IAC1、电枢电压VAC1、有功功率、功率因数，以及直流电源显示屏上的励磁电压和电流。</li>
		<li>测量并记录电机的转矩和转速。</li>
	</ol>
	</li>
	<li>关闭直流电源，将“启动/运行”开关拨回“启动”位置，并将可变变压器（VARIAC）调回0%。</li>
	<li>关闭三相断开开关。保持电路其余部分不变。</li>
</ol>
<img alt="带可变变压器、直流电源和机械耦合至直流测功机的同步电机示意图。" src="/files/ftp_upload/10168/10168fig1.jpg" data-altupdatedat="1761830439000" data-alt="图1"> 
图1：启动同步电机的实验装置示意图。<a href="//cloudfront.jove.com/files/ftp_upload/10168/10168fig1large.jpg" target="_blank">请点击此处查看此图的放大版本。</a>
3. 负载对转矩角的影响
<ol>
	<li>确保三相断路开关、同步电机开关“S1，“和直流电机开关“S2均处于关闭状态。
	<ol>
		<li>请注意，尽管“S”1位于同步电机侧，用于在直流电机端子间连接/断开“RL”负载。</li>
		<li>检查VARIAC是否处于0%。</li>
	</ol>
	</li>
	<li>连接图2所示的装置，并设置“R”L至 200 Ω。</li>
	<li>检查“启动/运行”开关是否处于“启动”位置。</li>
	<li>打开三相断路开关。</li>
	<li>迅速调高VARIAC输出，直至数字功率计读数约为115 V。</li>
	<li>打开125 V直流电源。确保所有连接均远离电源端子。</li>
	<li>按下电源启动按钮，并将电源输出设置为 125 V。</li>
	<li>将“启动/运行”开关拨至“运行”位置。</li>
	<li>记录电枢电流 我AC1，电枢电压 VAC1、有功功率、功率因数以及直流电源显示的励磁电压和电流。</li>
	<li>测量并记录该设备的扭矩和转速。</li>
	<li>将频闪灯保持在轴附近，并测量初始角度 δo.
	<ol>
		<li>设置频闪灯时，将其插入普通电源插座并打开电源。</li>
		<li>使用粗调旋钮，将频闪仪上的转速读数调整至接近 1,800 RPM，此为一台四极 60 Hz 电机的同步转速。同步转速以每分钟转数（RPM）计算，计算公式为 n=120xf/P 其中 f 频率和 P 是极的数量。</li>
		<li>将频闪灯对准电机轴的边缘，调节微调旋钮，直至轴看起来静止不动。当频闪灯的频率（或转速读数）与轴的转速相匹配时，人眼会误以为轴处于静止状态。</li>
	</ol>
	</li>
	<li>打开“S”1“并重复步骤 3.9 至 3.11，但将新角度测量为 δ”1.</li>
	<li>打开“S”2，重复步骤 3.9 至 3.11，但将新测得的角度记为 δ2.</li>
	<li>关闭“S”2”并更改“RL至 100 Ω。</li>
	<li>打开“S”2“并重复步骤 3.9 至 3.11，但将新角度测量为 δ”3.</li>
	<li>关闭直流电源，将“启动/运行”开关拨至“启动”位置，关闭“S”1以及“S2”，并将VARIAC调回至0%。</li>
	<li>关闭三相断路开关。保持电路其余部分不变。</li>
</ol>
<img alt="带可变变压器、直流电源、机械耦合和测功机系统的同步电动机装置示意图。" src="/files/ftp_upload/10168/10168fig2.jpg" data-altupdatedat="1761830439000" data-alt="图 2"> 
图 2：研究负载对转矩角影响的实验装置示意图。 <a href="//cloudfront.jove.com/files/ftp_upload/10168/10168fig2large.jpg" target="_blank">请点击此处查看此图的放大版本。</a>
4. 磁场电流对功率因数的影响
本部分研究V型曲线的一侧。
<ol>
	<li>确保三相断开开关、同步电机开关 S1 和直流电机开关 S2 均处于关闭状态。</li>
	<li>检查可变变压器（VARIAC）是否处于 0% 位置。</li>
	<li>连接如图 3 所示的电路，该电路与图 2 的唯一区别是增加了串联磁场电阻“RF”，并将“RL”设置为 200 Ω。</li>
	<li>将“RF”设置为 10 Ω 位置。本实验中无需测量“RF”的阻值，因为实验目的仅为调节励磁电流。</li>
	<li>检查“启动/运行”开关是否处于“启动”位置。</li>
	<li>打开三相断开开关。</li>
	<li>迅速增加可变变压器（VARIAC）的输出，直到数字功率计读数为 115 V。</li>
	<li>打开 125 V 直流电源。确保所有连接线均已远离电源接线端子。</li>
	<li>按下电源启动按钮，并将电源输出设置为 125 V。</li>
	<li>将“启动/运行”开关拨至“运行”位置。</li>
	<li>对于“RF” = 10、6、3 和 1 的每种情况，记录电枢电流 IAC1、电枢电压 VAC1、有功功率、功率因数，以及直流电源显示屏上的励磁电压和电流。</li>
	<li>测量并记录电机的转矩和转速。</li>
	<li>将“RF”重新设置为 10 Ω。</li>
	<li>打开“S1”，然后重复步骤 4.11 至 4.13。</li>
	<li>打开“S2”，然后重复步骤 4.11 至 4.13。</li>
	<li>关闭“S2”，并将“RL”更改为 100 Ω。</li>
	<li>打开“S2”，然后重复步骤 4.11 至 4.13。</li>
	<li>关闭直流电源，将“启动/运行”开关拨回“启动”位置，并将可变变压器（VARIAC）调回 0%。</li>
	<li>关闭三相断开开关，并拆除实验装置。</li>
</ol>
<img alt="用于与直流测功机机械耦合的三相可变变压器和同步电机示意图。" src="/files/ftp_upload/10168/10168fig3.jpg" data-altupdatedat="1761830439000" data-alt="图3"> 
图3：研究改变励磁电流影响的实验装置示意图。 <a href="//cloudfront.jove.com/files/ftp_upload/10168/10168fig3large.jpg" target="_blank">请点击此处查看此图的放大版本。</a>

同步电机常用于需要电机轴转速恒定且调速精度极高的场合。此类应用包括电子钟和硬盘驱动器，但也延伸至同步调相机，即运行于超前功率因数区域以向负载提供无功功率的同步电机。功率因数校正也是与同步调相机应用相关的术语。需要注意的是，最常见的同步电机是永磁同步电机，而最常见的同步发电机则是绕线转子同步发电机。

交流同步电机特性表征

来源：Ali Bazzi，康涅狄格大学电气工程系，斯托尔斯，康涅狄格州。
三相绕线转子同步电动机由于转子磁场需要电刷，因此不如永磁转子同步电动机普及。同步发电机则更为常见，大多数现有的发电厂都采用此类发电机，因为它们具有优异的频率和电压调节性能。同步电动机的优点在于其转速调节几乎为0%，这是因为转子转速与定子磁场转速完全相同，使得转子转速保持恒定，不受电机轴负载大小的影响。因此，它们非常适用于恒速运行的应用场合。
本实验的目的是理解三相同步电动机的启动概念、不同负载下的V形曲线（其中负载影响电动机的功率因数），以及负载对端电压与反电动势之间夹角的影响。

通过直流试验可估算直流相电阻，即在相端子与中性点之间施加直流电压时，直流电压与直流电流的比值。励磁电阻的测量方法类似，即向励磁绕组施加直流电压并测量励磁电流。同步电抗（Xs）、电机的反电动势（EA）及其相关常数 kφ 可通过输入电机的有功功率（P3φ）测量得到： P3φ=3VφEAcos(δ)/Xs（忽略定子电阻 Rs），并结合每相等效电路的基本功率传输方程（图4）求得。
V形曲线用于确定电源（电网）所观测到的电机功率因数。V形曲线表明，在特定条件下，电机能够提供无功功率（...

来源：Ali Bazzi，康涅狄格大学电气工程系，美国康涅狄格州斯托尔斯市。  
三相绕线转子同步电动机较少……

同步电机适用于需要转子转速恒定、不受轴负载变化影响的应用场景，在发电厂中几乎无处不在，用于调节频率和电压。同步电机由内部旋转的核心部分（称为转子）和外部静止的环形结构（称为定子）组成。转子的磁场是固定的，可通过永磁体或直流电源产生。在三相同步电机中，电流流入电机的定子，每一相分别连接到各自独立的一组定子线圈，从而产生与电源电流振荡相对应的独立旋转磁场。定子与转子的磁场相互耦合或锁定，使转子以与定子磁场旋转速率完全相同的速度旋转。本视频的主要目标是介绍三相同步电机，演示启动并实现转子与定子磁场锁定的操作步骤，并展示如何测定电机负载对转矩角影响的实验方法。为了克服定子与转子磁场对齐前的初始惯性，三相同步电机在启动时首先作为感应电动机运行。在此过程中，定子的旋转磁场在鼠笼式转子中感应出电流，进而在转子周围产生磁场并引发旋转。当电机转速接近同步转速时，直流电压被施加到励磁绕组上。此后，电磁励磁控制转子磁场。由于转子磁场被固定，转子与定子磁场相互锁定，实现转子-定子同步。因此，同步电机的转速由定子磁场的旋转速度决定，且与负载无关。尽管转子负载不会影响同步电机中转子的转速，但会导致转子磁极略微滞后于定子磁极。虽然电机仍以同步转速运行，这种角位移被称为转矩角，其值在负载较低时较小，在负载较高时较大。随着机械负载的增加，转矩角也随之增大，直至角度过大导致转子失去同步。此时的机械负载已超过电机所能承受的极限，该极限称为最大转矩（breakdown torque）。在已了解同步电机基本原理的基础上，我们将演示其启动、同步及特性表征的操作步骤。启动同步电机之前，需测试用于锁定转子与定子磁场的直流电源。首先，将低功率直流电源短路并开启电源。将电源输出电流调至1.8安培，然后关闭电源并断开短路连接。直流测试用于测量定子绕组电阻。首先，将直流电源的两个端子连接至同步电机的1号和4号端口，然后开启电源。记录通过这两个端口的直流电压和电流。根据需要调节电压，使电流达到1.8安培的限值。记录此时的电压值，然后关闭电源。按照上述方法，分别在2号与5号端口、以及3号与6号端口之间重复进行电压和电流的测量。最后，断开直流电源，完成直流测试。在该实验方案的下一步中，同步电机首先以感应电动机模式启动，然后使转子与定子的磁场锁定。首先，确认三相断路开关、同步电机开关以及直流电机开关均处于关闭状态。接着，检查可变变压器（variac）是否已调至零百分比输出电压。在设备断电的情况下，将可变变压器连接至三相电源插座，并按图示方式连接装置。然后，在交流同步电机转子轴上粘贴一小段胶带。最后，将数字功率计电流探头的量程设置为 5 至 100 A。现在，接通设备电源以启动电机。第一步，确认“启动-运行”开关处于“启动”位置；第二步，闭合三相断路开关；第三步，迅速调节可变变压器输出，直至数字功率计读数约为 115 伏特。这些测量值对应 A 相的相电压（线对中性点）和相电流，以确保功率因数测量值准确反映每相的功率因数。随后，测量电机在感应模式下的转矩。最后，使用频闪灯技术测量电机转速。有关该技术的更多信息，请参考《科学教育》视频“直流电机”（DC Motors）。在电机启动并完成初始参数测量后，即可进行同步操作。首先，打开 125 伏直流电源。然后，将“启动-运行”开关拨至“运行”位置。注意倾听电机声音的变化。随着转子磁场与定子旋转磁场的锁定，电机运行声音将变得更加平稳。当转子与定子磁场实现锁定（即同步）后，测量电枢电流和电压、功率及功率因数。接着，从直流电源显示屏读取励磁电压和电流值。随后，测量机械特性，包括转矩和转速。最后，关闭设备，首先关闭直流电源。然后，将“启动-运行”开关拨回“启动”位置，并将可变变压器调回零百分比输出。最后，断开三相断路开关。当直流电动机通过机械方式耦合至同步电机以提供机械负载时，可通过调节直流电动机的并励磁场电流来改变同步电机的转矩角。本实验方案旨在研究电动机励磁负载与转矩角之间的关系。在设备断电状态下，按照图示连接电路，并将并联负载电阻设置为2千欧姆。随后，按照前述方法启动设备，记录此前所述的电气与机械参数。接下来，在并励磁场加载的情况下记录转矩角。具体操作为：使用频闪仪将同步电机转轴的旋转视觉定格。通过“粗调”旋钮将频闪频率调节至约1800转/分钟，即四极60赫兹电机的同步转速。然后将频闪灯光对准电机转轴边缘，调节“细调”旋钮，直至转轴看起来静止不动。首先，在RL设为200欧姆、开关S1和S2均断开的情况下测量转矩角。随后，按以下步骤在并励磁场加载时重复测量转矩角：闭合开关S1，测量转矩角Δ1；再闭合开关S2，测量转矩角Δ2；最后，断开S2，将RL改为300欧姆，重新闭合S2，再次测量转矩角。全部测量完成后，按照前述方法关闭设备。直流相电阻是通过直流试验估算得到的，即在相端子与中性点之间施加直流电压和直流电流时，其电压与电流的比值。相电阻会导致电机中的损耗，并在电枢上产生电压降。励磁电阻的测量方法类似，通过向励磁绕组施加直流电压并测量励磁电流获得。励磁电阻控制励磁电流。在励磁电阻固定的情况下，可通过调节励磁电压来改变励磁电流。最后，通过调节直流电动机的并励励磁电流以改变机械负载，从而使转矩角增大。该电机的有功功率与转矩角之间的关系如图所示。这表明当转矩角为零时，输出功率达到最大。同步电机常用于需要电机轴转速恒定且调速精度要求较高的场合。三相绕线转子同步发电机是全球电能的主要来源。为了将某电厂的发电机与电网连接，发电机输出电压的三个因素必须与电网匹配，即幅值、频率和相序。虽然大型电厂通常使用自动同步装置，但在 JoVE 科学教育视频《交流同步电机同步》中演示了一种手动同步的简单方法。同步电动机也常用于一些简单设备，例如球磨机。球磨机是一种通过旋转装有微小金属球的圆柱体来混合和研磨物料的装置。金属球的撞击作用将置于圆柱体内的物料研磨成细粉。这类研磨设备常用于混合涂料等材料，或粉碎植物谷物等物质。您刚刚观看了 JoVE 关于交流同步电机特性介绍的视频。您现在应该理解交流同步电机的工作原理、如何启动和同步电机，以及电机负载对转矩角的影响。感谢观看。

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教育

JoVE Science Education

Engineering

工程学

Electrical Engineering

电气工程

交流同步电机特性

three-phase synchronous motor starting and v-curves

Three-phase synchronous motors and generators are important AC machines. Wound-rotor synchronous motors are less common than permanent magnet rotor synchronous motors because the rotor field uses brushes. Synchronous generators are much more common. They are used in most existing power plants because they provide excellent frequency and voltage regulation.

A synchronous motor runs at the same speed as the stator magnetic field. This gives it almost 0% speed regulation, so the rotor speed stays constant even when the shaft load changes. That makes synchronous motors a good choice for fixed-speed applications.

This experiment focuses on starting a three-phase synchronous motor and on V-curves. A V-curve shows how load changes the motor power factor. The study also looks at how load changes the angle between the terminal voltage and the back e.m.f. (electromotive force, or induced voltage).

Three-Phase Synchronous Motor Starting and V-Curves

three-phase-synchronous-motor-starting-and-v-curves

electrical safety precautions and basic equipment

electrical-safety-precautions-and-basic-equipment

Safe Handling of High-Voltage Lab Power

Safe handling of high-voltage lab power is essential in electric machine and power electronics experiments. These labs involve electrical currents, voltages, power, and energy that require extreme care. The systems used in this work can include three-phase AC voltage at 208 V, 230 V, or 480 V. They may also use up to 250 V DC and currents that can reach 10 A. These levels can be dangerous if handled without proper attention. Electrocution can happen when electricity passes through the body.

characterization of magnetic components

B-H Curves and Inductor Core Limits

Magnetic components such as inductors and transformers depend on the core material around their windings. In this experiment, students get hands-on experience with these parts from both a design view and a material view. The work focuses on B-H curves, which show the magnetic behavior of a material. A B-H curve describes the magnetic flux density the core can support as current flows through the windings. It also helps show the limit before magnetic saturation occurs. Magnetic saturation...

introduction to the power pole board

Power Pole Board for DC/DC Converter Labs

The HiRel Power Pole Board is a flexible tool for studying DC/DC converters. A DC/DC converter changes direct-current voltage and current from one level to another. In many cases, voltage conversion is the main goal. This board supports several converter types on one platform. It can be used to examine boost converters, which step voltage up, and buck converters, which step voltage down. It also helps students study buck-boost converters, which can step voltage up or down. The board is also...

dc/dc boost converter

Stepping Up DC Voltage with Boost Converters

DC voltage can be increased with a boost converter. This step-up circuit is useful in many applications where a DC source must be raised without first converting it to AC, using a transformer, and then rectifying the transformer output. A boost converter uses an inductor as an energy storage device. The inductor supports the output with extra energy in addition to the DC input source. That added energy raises the output voltage. This experiment studies several characteristics of a boost...

dc/dc buck converter

Buck Converter Step-Down DC Voltage

A DC/DC buck converter steps down DC voltage in an efficient, regulated way. Unlike transformers, which easily raise or lower AC voltage and current, DC systems need switching power converters to change voltage levels. The buck converter works by chopping the input DC voltage with a series input switch. An L-C low-pass filter then smooths the chopped signal and extracts the average output voltage. A diode gives the inductor current a path when the switch is off during part of the switching...

flyback converter

Flyback Converter Voltage Step-Up and Step-Down

A flyback converter is a buck-boost converter that can both step voltage up and step it down. It also provides electrical isolation between the input and the output by using a coupled inductor, or flyback transformer. The coupled inductor acts like a transformer with a turns ratio, but it also stores energy through the air gap. This setup gives the converter both voltage step-up and step-down capability. In the experiment, the converter is studied in open-loop operation with a manually set...

single phase transformers

Single Phase Transformer Testing

Single-phase transformers step up or step down AC voltage in electric power systems. They are stationary electric machines with primary and secondary coils, also called windings. The primary winding receives the applied voltage, and the secondary winding delivers the changed voltage. Inside the transformer, current in one winding creates magnetic flux in the core. This flux links the two windings and transfers energy between them. With AC current, the changing flux induces voltage in the...

single phase rectifiers

AC to DC Conversion with Rectifiers

Rectifiers convert AC power into DC power for electronic circuits. A DC power supply provides unidirectional voltage and current. Batteries can do this, but they are limited by lifetime and cost. Using a rectifier is another way to turn AC line power into DC power. A rectifier is a device that lets current pass in one direction and blocks it in the other. It works after a forward voltage threshold is reached. Rectifiers may use a diode, a silicon controlled rectifier, or other silicon P-N...

thyristor rectifier

Controlling SCR Half-Wave Rectification

Thyristors, also called silicon controlled rectifiers (SCRs), are used to control current in a rectifier circuit. Like diodes, they let current pass from the anode to the cathode and block current in the opposite direction. Unlike a diode, a thyristor can be turned on with a gate terminal that receives a small current pulse. A thyristor is a four-layer device with alternating n-type and p-type layers. These layers form a PNPN structure with three junctions. The device has three terminals. The...

single phase inverter

DC to AC Conversion with Half-Bridge Inverters

DC to AC conversion is the main idea behind a power inverter. DC power flows in one direction, while AC current changes direction at about 50-60 Hz. Many electronic devices are designed to run on AC power, so a DC source must be inverted before it can be used with them. An inverter makes this change through switching action. The switches repeatedly flip the polarity of the input DC source at the output, or load side, for part of a switching period. A typical power inverter needs a stable DC...

dc motors

DC Motors and Generator Action

DC machines use direct current and direct voltage to create motion or generate electricity. They were the first machines of this kind to be invented. A DC machine works with two magnetic fields that are controlled by DC currents, and the same machine can be set up as either a motor or a generator when the right field excitation is available. In a DC machine, the field is usually on the stator side and the armature is on the rotor side. That arrangement is the reverse of what is found in many...

ac induction motor characterization

Three-Phase Motor Equivalent Circuit Tests

Three-phase induction motor testing can be used to find equivalent circuit parameters. The experiment uses the per-phase equivalent circuit to model the motor. This model keeps the important behavior of the original system and makes calculations easier. The procedure uses tests similar to those used in transformer characterization. These measurements help estimate the motor's circuit values from its electrical response. The experiment also aims to operate the motor in the linear torque-speed...

vfd-fed ac induction machine

Variable Frequency Drive Speed Control

Variable frequency drives, or VFDs, control the speed of AC induction motors. They are a type of adjustable speed drive and are becoming standard equipment for powering most AC induction motors. In industrial and automation settings, VFDs can provide strong control of motor speed, torque, or position. This experiment focuses on speed control with open-loop operation. It uses constant voltage-to-frequency ratio control, also called V/f control. The motor usually operates at a rated stator flux,...

ac synchronous machine synchronization

Grid Connection of AC Synchronous Generators

AC synchronous generators are a major source of electrical power worldwide. They are three-phase, wound-rotor machines that are used in many power plants. These generators need a prime mover and an exciter to produce power. A prime mover is the device that spins the generator, often a turbine driven by fluid. That fluid can come from water flowing from a dam through a long nozzle or from steam made by burning coal. Most power plants use synchronous generators, including coal, nuclear, natural...

ac synchronous machine characterization

Three-phase synchronous motors and generators are important AC machines. Wound-rotor synchronous motors are less common than permanent magnet rotor synchronous motors because the rotor field uses brushes. Synchronous generators are much more common. They are used in most existing power plants because they provide excellent frequency and voltage regulation. A synchronous motor runs at the same speed as the stator magnetic field. This gives it almost 0% speed regulation, so the rotor speed stays...

electrical engineering

本系列从电气安全视频开始, 介绍了电气实验室中常用设备的最佳实践。随后的视频介绍了电感器、变压器、变流器、整流器和逆变器等元素。

Explore how three-phase synchronous motors start, why they keep nearly constant speed, and how V-curves show the effect of load on power factor and back e.m.f.

Three-Phase Synchronous Motor Starting and V-Curves | JoVE K12

Ali Bazzi

Overview

Principles of AC Synchronous Motors

DC Test

Starting the AC Synchronous Machine

Effect of Load on Torque Angle

Results

Applications

Summary

Newton's Second Law

Newton&#39;s second law is closely related to his first law of motion. It mathematically gives the cause-and-effect relationship between force and changes ...

Second Law: Motion under Same Force

Newton&#39;s laws can be applied to bodies at rest and bodies in motion. Newton&#39;s first law is applied to bodies in equilibrium, whereas the second ...

Force and Acceleration

Source: Nicholas Timmons,&#160;Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of California, Irvine, ...

second-law-motion-under-same-acceleration

Second Law: Motion under Same Acceleration

Newton&#39;s second law of motion applies to bodies moving under the same acceleration. For example, when a baggage tractor pulls luggage carts, each cart ...

Newton's Laws of Motion

Source: Andrew Duffy, PhD, Department of Physics, Boston University, Boston, MA
This experiment examines at various situations involving two interacting ...

Newton's Law of Motion

When we observe objects around us, one question that comes to mind is why they move or stay still. The answer to this question can be explained using ...

Analyze data to support the claim that Newton's second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass, and its acceleration.

P-PS2-1

Force and Momentum

Force and momentum are intimately related. Force acting over time can change momentum, and Newton&#39;s second law of motion can be stated in its most ...

Internal and External Forces

Newton&#39;s first law states that a net external force causes a change in motion. External forces act on an object or system, originating outside of the ...

Conservation of Momentum: Introduction

The total momentum of a system consisting of N interacting objects is constant in time or is conserved. A system must meet two requirements for its ...

Force

Forces affect every moment of our life. Our bodies are held to the Earth by force, and they are held together by the forces of charged particles. When we ...

Conservation of Momentum

Conservation of Momentum: Problem Solving

Solving problems using the conservation of momentum requires four basic steps:

	Identify a closed system, where the total mass is constant, and no net ...

conservation-of-linear-momentum-for-a-system-of-particles

Conservation of Linear Momentum for a System of Particles

In a game of billiards, when the cue ball strikes a stationary ball, it transfers some of its momentum to the stationary ball. The cue ball slows down, ...

principle-of-linear-impulse-and-momentum-for-a-system-of-particles

Principle of Linear Impulse and Momentum for a System of Particles

Consider a system of particles moving relative to an inertial frame of reference.
The equation of motion for such a system can be written as the sum of ...

Use mathematical representations to support the claim that the total momentum of a system of objects is conserved when there is no net force on the system.

P-PS2-2

principle-of-linear-impulse-and-momentum-for-a-single-particle

Principle of Linear Impulse and Momentum for a Single Particle

Linear momentum is a fundamental concept in physics that describes the motion of an object. It is a vector quantity, having a magnitude equal to the ...

principle-of-angular-impulse-and-momentum-problem-solving

Principle of Angular Impulse and Momentum: Problem Solving

Consider a ball of mass m, attached to a massless rod of known length, subjected to a time-dependent torque. If the initial velocity of the mass is known, ...

Linear Momentum

The term momentum is used in various ways in everyday language, most of which are consistent with the precise scientific definition. Generally, momentum ...

principle-of-angular-impulse-and-momentum

Principle of Angular Impulse and Momentum

The angular impulse and momentum principle provides insights into how forces applied at a distance from an object&#39;s rotational axis influence its ...

principle-linear-impulse-momentum-for-single-particle-problem

Principle of Linear Impulse and Momentum for a Single Particle: Problem Solving

Consider a massless pulley system consisting of a wooden box and a cylinder of known masses. Determine the speed of the attached objects at a specific ...

Angular Momentum

Angular momentum describes the rotational motion of an object.
It is defined as the moment of the object&#39;s linear momentum about a specific point O.
...

relation-between-moment-of-a-force-and-angular-momentum

Relation Between Moment of a Force and Angular Momentum

In a spinning top, applying a force at a distance from the center creates torque, which changes the angular momentum of the top, causing it to spin.
The ...

Apply scientific and engineering ideas to design, evaluate, and refine a device that minimizes the effect of a force on a macroscopic object during a collision.

P-PS2-3

Gravitation

In the years before Newton, a general belief prevailed that different laws governed objects in the sky than objects on Earth. When Kepler wrote down the ...

/files/media/science-education/science-education-thumbs/14716.jpg

Newton's Law of Gravitation

Our everyday observation tells us that all objects close to the Earth naturally tend to fall to the ground. Early philosophers assumed that this downward ...

gravitation-between-spherically-symmetric-masses

Gravitation Between Spherically Symmetric Masses

The gravitational potential energy between two spherically symmetric bodies can be calculated from the masses and the distance between the bodies, ...

/files/media/science-education/science-education-thumbs/14717.jpg

Gravity between Spherical Bodies

Newton&#39;s law of gravitation describes the gravitational force between any two point masses. However, for extended spherical objects like the Earth, ...

Coulomb's Law

Experiments with electric charges have shown that if two objects each have an electric charge, they exert an electric force on each other. The magnitude ...

comparison-between-electrical-and-gravitational-forces

Comparison Between Electrical And Gravitational Forces

There are four fundamental forces in nature: the gravitational force, the electromagnetic force, the strong nuclear force, and the weak nuclear force. To ...

Newton's Law of Gravitational Attraction

Sir Isaac Newton established the universality of the law of gravitational attraction based on empirical evidence and inductive reasoning. He published his ...

Newton's Law of Universal Gravitation

Source: Ketron Mitchell-Wynne, PhD,&#160;Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of ...

Use mathematical representations of Newton's law of gravitation and Coulomb's law to describe and predict the gravitational and electrostatic forces between objects.

P-PS2-4

Types of Forces

In most situations, forces can be grouped into two categories: contact forces and field forces.&#160; Contact forces occur as a result of direct physical ...

Magnetic Fields

Source: Yong P. Chen, PhD, Department of Physics &#38; Astronomy, College of Science, Purdue University, West Lafayette, IN
Magnetic fields can be ...

Electric Charge in a Magnetic Field

Source: Andrew Duffy, PhD, Department of Physics, Boston University, Boston, MA
This experiment duplicates J.J. Thomson's famous experiment at the end of ...

Electric Fields

Source: Yong P. Chen, PhD, Department of Physics &#38; Astronomy, College of Science, Purdue University, West Lafayette, IN
An electric field is generated ...

Electromagnetic Fields

Electric fields generated by static charges, often referred to as electrostatic fields, are characteristically different from electric fields created by ...

Magnetic Field Due to Two Straight Wires

Consider two parallel straight wires carrying a current of 10 A and 20 A in the same direction and separated by a distance of 20 cm. Calculate the ...

Energy Carried By Electromagnetic Waves

Anyone who has used a microwave oven knows there is energy in electromagnetic waves. Sometimes, this energy is obvious, such as in the summer sun&#39;s ...

Energy Stored in Capacitors

A parallel plate capacitor connected to a battery develops a potential difference across its plates.
By integrating the equation relating voltage and ...

Power and Energy

Energy is the total work required to drive the current through the circuit.
A rise in voltage results in more work done, passing more current, resulting ...

Voltage

The movement of electrons in a conductor requires some form of energy or work, usually provided by an external force, like a battery. This force is called ...

Electromotive Force

Electromotive force (emf) is the force that causes current to flow from a higher to a lower&#160; potential. The term &#34;electromotive ...

Electrical Energy

Using electric appliances for a longer period of time consumes more electrical energy and results in a higher electric bill. The energy produced by the ...

Electrical Current

Electrical current is defined as the rate at which charge flows. When there is a large current present, such as that used to run a refrigerator, a large ...

Electric Potential Energy

When an electric field accelerates a free positive charge q, it is given kinetic energy. The process is analogous to an object accelerated by a ...

Electrical Power

Electric power is the product of current and voltage, represented in units of joules per second, or watts. For example, cars often have one or more ...

Plan and conduct an investigation to provide evidence that an electric current can produce a magnetic field and that a changing magnetic field can produce an electric current.

P-PS2-5

sources-and-properties-of-electric-charge

Sources and Properties of Electric Charge

All objects we see around us consist of atoms, which combine to form molecules. The lightest element in the universe is hydrogen, and a hydrogen atom ...

Electric Charges

From lightning during thunderstorms to electronic devices, the phenomenon of electromagnetism is all around us. The electromagnetic force is one of the ...

Electron Behavior

Electrons are negatively charged subatomic particles attracted to and orbit around the positively-charged nucleus of an atom. They reside in spaces ...

Communicate scientific and technical information about why the molecular-level structure is important in the functioning of designed materials.

Three-Phase Synchronous Motor Starting and V-Curves

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