Name: bicycle torque and moment about an axis
Uploaded: 2023-09-22T11:49:21.000Z
Duration: 1 min 28 s
Channel: JoVE

Consider a cyclist riding a bicycle and applying force on the pedal to turn the wheel. When a force is exerted on the pedal, the attached chain exerts a force on the wheel&#39;s cogs. The wheel rotates around its axle, so the axis of rotation passes through it.
The moment of a force along the axis measures how much the force causes an object to rotate around a specific point or axis.
In this case, the wheel rotates about the y-axis in the x-z plane. Here, the moment arm or the perpendicular distance between the axis of rotation and the line of action of the force is the radius of the cogs.
So the moment of a force about the y-axis is equal to Frsin&#952;.
Since the force is tangential, the angle between the force vector and the radius is 90 degrees.
In a bicycle, the moment of force can be multiplied by the angular velocity of the axle to obtain the power generated by the wheel rotation.

moment of a force about an axis: scalar

Moment of a Force About an Axis: Scalar

The moment of a force about an axis is a crucial concept in mechanics that helps determine an object's rotational motion around a specific point or axis. The moment of force can be calculated using scalar analysis, which involves considering the perpendicular distance between the axis of rotation and the line of action of the force or simply the moment arm.
To better understand the concept of moment of force, consider the example of a cyclist riding a bicycle. When the cyclist applies force on the pedal, the attached chain exerts a force on the wheel's axle, causing it to rotate. Here, the axis of rotation passes through the wheel's axle and the moment arm is the radius of the axle. In this case, the moment of the force about the axis of rotation is given by:
<img alt="Static equilibrium equation \(M_O = Fr\sin\theta\) in physics. Diagram of moment calculation." src="/files/ftp_upload/14258/14258_Equation_1v2.svg" style="text-align: center; height: 13px;" data-altupdatedat="1761830439000" data-alt="Equation 1">
where, F is the applied force, r is the radius of the axle, and θ is the angle between the force vector and the radius. Since the force is tangential, the angle between the force vector and the radius is 90 degrees.
In a bicycle, the moment of force can be multiplied by the angular velocity of the axle to obtain the power generated by the wheel rotation. The moment of force is essential in designing various structures and machines, including bicycles, automobiles, and aircraft, to ensure their stability and safety.

The moment of a force about an axis is a crucial concept in mechanics that helps determine an object&#39;s rotational motion around a specific point or ...

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bicycle torque and moment about an axis

The moment of a force about an axis describes how a force can make an object turn around a fixed line. In scalar analysis, the moment is found from the perpendicular distance between the axis of rotation and the line of action of the force. That distance is called the moment arm.

A bicycle gives a clear example of this idea. When the cyclist pushes on the pedal, the chain applies a force to the wheel’s axle and makes it rotate. The axis of rotation passes through the axle, and the moment arm is the axle radius.

For this case, the moment of force about the axis depends on the force, the radius, and the angle between the force vector and the radius. Because the force is tangential, that angle is 90 degrees. The moment of force can also be multiplied by the angular velocity of the axle to find the power produced by the wheel rotation.

This concept is important in the design of bicycles, automobiles, and aircraft. Engineers use it to help maintain stability and safety in these machines and structures.

Bicycle Torque and Moment About an Axis

moment of a force: scalar formulation

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Torque, or the moment of a force, describes how a force can make an object turn about an axis. It is a vector quantity, so it has both size and direction. This idea is important in physics, mechanics, and engineering. A simple flywheel example shows how torque works. The flywheel rotates about point O when a force is applied to it. The moment arm is the perpendicular distance from point O to the line of action of the force. The moment, in newton-meter (N-m), is found by multiplying the force...

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principle of moments

Resolving Forces in Moment Calculations

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Torque About an Axis in 3D Systems

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The moment of a force about an axis describes how a force can make an object turn around a fixed line. In scalar analysis, the moment is found from the perpendicular distance between the axis of rotation and the line of action of the force. That distance is called the moment arm. A bicycle gives a clear example of this idea. When the cyclist pushes on the pedal, the chain applies a force to the wheel’s axle and makes it rotate. The axis of rotation passes through the axle, and the moment arm...

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key terms and concepts

Learn how the moment of a force about an axis is found with scalar analysis, using a bicycle axle example and its link to rotational power.

Bicycle Torque and Moment About an Axis | JoVE K12

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Bicycle Torque and Moment About an Axis

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