Pure Rotation - Example Problem 4.2-8

The square plate rotates about the fixed pivot O. At the instant represented, the direction of the angular velocity, ω, and angular acceleration, α, of the plate are shown in the figure. Determine the velocity and acceleration of points A and B in the x-y coordinate frame.

Given:

• ω
• α
• Dimensions of the plate.

Find:

• v_A, a_A
• v_B, a_B

So far we have used the n-t coordinate equations to calculate the velocity and acceleration of a point on a rigid body undergoing pure rotation.

v_A = r_Aωe_t           a_A = r_Aαe_t + r_Aω²e_n

Draw the n-t coordinate axes for points A and B. Click on the figure to see these coordinates.

Notice that equating the n_A-t_A coordinate axes to the x-y coordinate axes is easy, but it is not so easy to equate the n_B-t_B coordinate axes. Therefore, the above equations may not be simple to use. For situations where we are working in a coordinate system other than the n-t coordinate system, it may be advantageous to use the cross product versions of the velocity and acceleration equations.

v_A = ω x r_A/0          a_A = α x r_A/0 - ω₀²r_A/0

Which is the correct velocity and acceleration equation for point A?