Answer to Question #303323 in Mechanics | Relativity for Amit

Question

The average angular acceleration of a stone lodged in a rotating car wheel is 100 rads .What will the stone’s final angular speed be after 3.0 s, if it starts

From rest? Also calculate its angular displacement during this time.

Answer 1

Explanations & Calculations

$\qquad\qquad \begin{aligned} \small \omega_f&=\small \omega_i+\alpha \Delta t\\ &=\small 0+100 \,rad\,s^{-2}\times 3.0\,s\\ &=\small 300.0\, rad\,s^{-1}\\ \\ \small \theta &=\small \omega_i \Delta t+\frac{1}{2}\alpha \Delta t^2 \\ &=\small 0+\frac{1}{2}\times 100\,rad s^{-2}\times (3.0\,s)^2\\ &=\small 450\,rad \end{aligned}$

• Angular displacement is noted by $\small \theta$