Answer to Question #257525 in Mechanics | Relativity for Ashu

Question

The average angular acceleration of a s tone lodged in a rotating car wheel is 100 rads -2 what will the stones final angular speed be after 3.0 s if it starts from rest ? Also calculate it's angular displacement during this time

Answer 1

Explanations& Calculations

• Assuming the stone would remain in contact with the tyre without dislodging from it,

a)

• Apply $\small \omega_f = \omega_i +\alpha t$ for the motion, you can compute the final angular velocity.

$\qquad\qquad \begin{aligned} \small\omega_f&=\small 0+100\,rads^{-2}\times3.0\,s\\ &=\small \bold{300\,rads^{-1}} \end{aligned}$

b)

• Apply $\small \theta= \omega_it+\frac{1}{2}\alpha t^2$ for the motion, you can compute the angular displacement of the stone.

$\qquad\qquad \begin{aligned} \small \theta&=\small 0\times3.0\,s+0.5\times(100\,rads^{-2})\times(3.0\,s)^2\\ &=\small \bold{450\,rad} \end{aligned}$

• This means the stone has completed a full rotation ($\small 2\pi \,rad = 360^0$ ) and another quarter ($\small \pi/2\,rad =90^0$) during this 3 seconds.