Name: velocity of point b in a rotating frame
Uploaded: 2024-03-07T13:22:24.000Z
Duration: 1 min 25 s
Channel: JoVE

Consider a member AB in linear motion. Simultaneously point B&#160; rotates around point A.
The position vectors of A and B are determined using a stationary reference frame.
The relative position of point B with respect to point A is expressed using an additional frame of reference x&#39;y&#39;, which translates and rotates with respect to the fixed frame.
The velocity of point B is a vector sum of the absolute velocity of point A and the relative rotational velocity of point B with respect to point A.
The relative velocity of point B has two terms. The first term represents the velocity components of point B relative to the rotating frame of reference.
The second component signifies the rate of change of the unit vectors of the rotating frame and can be expressed in terms of angular velocity.
So, the absolute velocity of point B is the sum of the absolute velocity of point A, the relative velocity of point B in the rotating frame, and the angular velocity effects caused by the rotating frame.

relative motion analysis using rotating axes

Relative Motion Analysis using Rotating Axes

Consider a component AB undergoing a linear motion. Along with a linear motion, point B also rotates around point A. To comprehend this complex movement, position vectors for both points A and B are established using a stationary reference frame.
However, to express the relative position of point B relative to point A, an additional frame of reference, denoted as x&#39;y&#39;, is necessary. This additional frame not only translates but also rotates relative to the fixed frame, making it instrumental in understanding the relative position. The velocity of point B is then calculated as a vector sum of the absolute velocity of point A and the relative rotational velocity of point B with respect to point A. The relative velocity of point B is made up of two terms.
The first term represents the velocity components of point B, but relative to the rotating frame of reference. The second term, on the other hand, signifies the rate of change of the unit vectors of the rotating frame. This can be expressed in terms of angular velocity.
Therefore, in conclusion, the absolute velocity of point B is determined by adding the absolute velocity of point A, the relative velocity of point B in the rotating frame, and the effects caused by the angular velocity within the rotating frame. This comprehensive approach allows for a more accurate and nuanced understanding of the movements within the system.

Consider a member AB in linear motion. Simultaneously point B&#160; rotates around point A.
The position vectors of A and B are determined using a ...

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Mechanical Engineering

Unit 1

Planar Kinematics of a Rigid Body

KEY TERMS AND CONCEPTS

velocity of point b in a rotating frame

A rotating frame of reference helps describe the motion of point B on a moving member AB. The member has linear motion, and point B also rotates around point A. To track that motion, position vectors for A and B are first written in a fixed reference frame.

A second frame, x'y', is then used to show the position of point B relative to point A. This frame both translates and rotates with the system. That makes it useful for analyzing the relative position more clearly.

The velocity of point B is found by adding the absolute velocity of point A and the relative rotational motion of point B with respect to A. The relative velocity of point B has two parts. One part gives the motion of point B in the rotating frame, and the other part comes from the changing direction of the unit vectors in that frame.

The second part can be written using angular velocity. In the end, the absolute velocity of point B comes from the velocity of point A, the relative velocity of point B in the rotating frame, and the effect of angular velocity in that frame. This approach gives a more complete picture of the motion in the system.

Velocity of Point B in a Rotating Frame

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A rotating frame of reference helps describe the motion of point B on a moving member AB. The member has linear motion, and point B also rotates around point A. To track that motion, position vectors for A and B are first written in a fixed reference frame. A second frame, x'y', is then used to show the position of point B relative to point A. This frame both translates and rotates with the system. That makes it useful for analyzing the relative position more clearly. The velocity of point B...

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key terms and concepts

Learn how a rotating frame of reference is used to find the velocity of point B from point A, relative motion, and angular velocity in a moving member AB.

Velocity of Point B in a Rotating Frame | JoVE K12

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Velocity of Point B in a Rotating Frame

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