Question

A drum rotates around its central axis at an angular velocity of 12.60 rad/s. If the drum then slows at a constant rate of 4.20 rad/s 2 , (a) how much time does it take and (b) through what angle does it rotate in coming to rest

Answer 1

Answer:

(a) t=3s

(b) β=18.9rad

Explanation:

Given data

$wo_{angular-velocity}=12.60 rad/s\\ \alpha_{angular-acceleration}=-4.20rad/s^{2}$

Part(a)

From the equation of angular motion to find time

So:

$w=w_{o}+\alpha t\\0=12.60rad/s+(-4.20rad/s^{2} ) t\\-4.20 t=-12.60\\t=3s$

Part(b)

From the equation of simple motion to find angle β

So

$\beta=w_{o}t+(1/2)\alpha t^{2}\\\beta=(12.60rad/s)(3)+(1/2)(-4.20rad/s^{2} ) (3s)^{2}\\ \beta =18.9rad$