Name: acceleration of point b in rotating axes
Uploaded: 2024-03-07T13:22:24.000Z
Duration: 1 min 22 s
Channel: JoVE

Consider member AB undergoing linear motion and simultaneous rotation about point A. The velocity of point B is expressed as the sum of the velocity of point A and the relative velocity of point B in the rotating frame and the angular velocity effects caused by the rotating frame.
Differentiating with respect to time gives the acceleration of point B. The first term is the linear acceleration of point A measured from a fixed frame.
The second term is the cross product of the angular acceleration with the position vector rBA.
The third term is the cross product of angular velocity and the rate of change of position vector rBA. This term can be expanded using a distributive property of vector product.
The last term is the time derivative of angular velocity effects caused by the rotating frame of reference.
Here, the first two terms denotes the acceleration of point B in the rotating frame of reference. The last two terms can be simplified to get the final equation for the acceleration of point B.

relative motion analysis using rotating axes - acceleration

Relative Motion Analysis using Rotating Axes - Acceleration

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. 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.
Time differentiation is employed in order to understand the acceleration of point B. The first term derived from this process represents the linear acceleration of point A, gauged from a stationary frame. The second term is identified as the cross-product of the angular acceleration and the position vector determining the relative position of point B with respect to point A, rBA. Thereafter, the third term presents itself as the cross product of angular velocity and the rate of change of the position vector rBA. This term can be further expanded using the distributive property of vector products. The final term is the time derivative of the effects of angular velocity caused by the rotating frame of reference.
In this scenario, it is important to note that the initial two terms signify the acceleration of point B within the rotating frame of reference. Meanwhile, the last two terms can be simplified to derive the final equation for the acceleration of point B, thus providing a comprehensive understanding of its movement.

Consider member AB undergoing linear motion and simultaneous rotation about point A. The velocity of point B is expressed as the sum of the velocity of ...

relative-motion-analysis-using-rotating-axes-acceleration

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JoVE Core

Mechanical Engineering

Unit 1

Planar Kinematics of a Rigid Body

KEY TERMS AND CONCEPTS

acceleration of point b in rotating axes

Acceleration of point B is found by analyzing a member AB that moves linearly and also rotates about point A. The motion is described with position vectors for points A and B in a fixed reference frame. This setup helps separate the motion of the point from the motion of the rotating frame.

The absolute velocity of point B is written as the velocity of point A plus the relative velocity of point B in the rotating frame. It also includes the effect of angular velocity in that rotating frame. To find acceleration, the velocity expression is differentiated with respect to time.

That differentiation gives the linear acceleration of point A measured from the stationary frame. It also gives the cross product of angular acceleration and the relative position vector rBA. Another term is the cross product of angular velocity and the time rate of change of rBA. This term can be expanded using the distributive property of vector products.

The final term comes from taking the time derivative of the angular-velocity effects in the rotating frame. The first two terms describe the acceleration of point B within the rotating frame. The last two terms can then be simplified to obtain the final equation for the acceleration of point B. This gives a full vector picture of how point B moves.

Acceleration of Point B in Rotating Axes

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key terms and concepts

Learn how acceleration of point B is derived for a member that both translates and rotates, using position vectors, angular velocity, and time differentiation.

Acceleration of Point B in Rotating Axes | JoVE K12

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Acceleration of Point B in Rotating Axes

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