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?

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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?

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Expert Answer

Step 1

Given information:

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R 0.25 m 0-800 rad 0 — 400 гad -100 m/s 2 а

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Step 2

Here, R is the radius of the disc, θ is the total angle rotated by the disc to come to stop,θ­1 is the initial angular displacement of the disc with constant angular acceleration(α1) and ac is the maximum centripetal acceleration.

Write the formula for centripetal acceleration and plug the required values to find the maximum velocity(vmax) of any point of the disc.

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2 V. max ac R |a_R max (100 m/s2)(0.25m) max = 5 m/s max

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Step 3

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

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max max (5 m/s) (0.25 m = 20 rad/s

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