Question

A merry-go-round rotates from rest with an angular acceleration of 1.11 rad/s2. How long does it take to rotate through (a) the first 1.85 rev and (b) the next 1.85 rev?

Please include an explanation

Answer 1

Given merry-go-round rotates from rest

so initial angular velocity

acceleration ,

(a) How long does it take to rotate through the first 1.85 rev.

Convert revolution to radians

We know

----------------(1)

ANSWER:

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(b)How long does it take to rotate through the next 1.85 rev?

1.85 rev +1.85rev =3.7 rev

There are two options: we can find time taken to complete 3.7 rev starting from rest and subtract time taken for first 1.85rev ( time from answer (a) )

OR

Find velocity after first 1.85 rev , then take that as initial velocity for next 1.85 rev and use equation from Part (a). Equation (1)

First Option is simpler

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Convert revolution to radians

We know

  

Time for 2nd 1.85 rev =

ANSWER:

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