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Chapter 10: Q9P (page 287)

A drum rotates around its central axis at an angular velocity of 12.60rad/s. If the drum then slows at a constant rate of 4.20rad/s2.

(a) how much time does it take and

(b) through what angle does it rotate in coming to rest?

Short Answer

Expert verified

a. The time required to slow down is3.00 s

b. The angle of the rotation when it coming to rest is18.9rad

Step by step solution

01

Listing the given quantities

Angular velocity of drum 12.60rad/s

Rate of slowdown α is4.20rad/s2.

02

Understanding the concept of angular velocity

We can use the kinematic equations

Formula:

ω=ω0+αtθ=ω0t+12αt2

03

Calculation of time required to slow down

(a)

t=-ω0α=3.00 s

The time required to slow down is3.00 s

04

Calculation of angle of the rotation when it coming to rest

(b)

θ-θ0=−ω022α=18.9rad

The angle of the rotation when it coming to rest is18.9rad

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