Question

A flywheel rotates with a constant retardation due to breaking from t=0to t=10 seconds. it made 400 revolutions . At time t=8 sec , it's angular velocity was 45πrad/sec. Determine

1 . Value of constant ratardation.

2. Total time taken to come to rest.

3. Total revolution made till it comes to rest.

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Answer 1

$\alpha =?\\ t_i= 0s\\ t_t = 10s\\ \omega= 0\ rad/s\\ \theta= 400\ rev= \dfrac{400}{2π}\ rad=\dfrac{200}{π}\ rad$

a.

$t= 8s\\ \omega = 45π\ rad/s$

from,

$\omega= \omega_o + \alpha t\\ 0 =45π + \alpha (2)\\$

$\alpha = \dfrac{-45π}{2} = -22.5π\ rad/s²$

b.

from,

$\omega² = \omega_o²+ 2\alpha s\\ 0 =\omega_o² + 2(-22.5π)(\dfrac{200}{π})\\ \omega_o= \sqrt{9000}= 94.87\ rad/s$

3.

Total revolution ($\theta$) = $400\ rev= \dfrac{400}{2π}\ rad$

$= 63.7\ rad$