Question

Asked Nov 1, 2019

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A disk, with a radius of 0.25 m, is to be rotated like a merry-go-round through 800 rad, starting from rest, gaining angular speed at the constant rate α1 through the first 400 rad and then losing angular speed at the constant rate -α1 until it is again at rest. The magnitude of the centripetal acceleration of any portion of the disk is not to exceed 100 m/s2. (a) What is the least time required for the rotation? (b) What is the corresponding value of α1?

Step 1

Given information:

Step 2

Here, *R* is the radius of the disc, *θ* is the total angle rotated by the disc to come to stop,*θ _{1}* is the initial angular displacement of the disc with constant angular acceleration(

Write the formula for centripetal acceleration and plug the required values to find the maximum velocity(*v _{max}*) of any point of the disc.

Step 3

Find maximum angular velocity(*ωmax*) correspond to the maximu...

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