Answer to Question #294233 in Mechanics | Relativity for Tiana

Question

A ball rolls up in an inclined plane with initial angular velocity 100.

(a) if its radius is r. What is it initial line velocity? After a time t the ball stops.

(b) what is it angular retardation

(c) what is the angular displacement before its stops

Answer 1

Explanations and Calculations

a)

• Initial linear velocity is $\small V=r\omega=100r$

b)

• If the angular retardation is $\small \alpha$ ,

$\qquad\qquad \begin{aligned} \small \omega_f&=\small \omega_i+\alpha.t\\ \small \alpha&=\small \frac{0-100}{t}\\ &=\small -\frac{100}{t} \end{aligned}$

c)

• If the angular displacement is $\small \theta,$

$\qquad\qquad \begin{aligned} \small \theta&=\small \omega.t+\frac{1}{2} \alpha t^2\\ &=\small 100t-\frac{1}{2}\times\frac{100}{t}\times t^2\\ &=\small 100t-50t\\ &=\small 50t \end{aligned}$