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Chapter 4: Q.74 (page 109)

A 6.0cm-diameter gear rotates with angular velocity role="math" localid="1647955750668" ω=(2.0+12t2)rad/s, where t is in seconds. At role="math" localid="1647955660518" t=4.0s, what are:

a. The gear’s angular acceleration?

b. The tangential acceleration of a tooth on the gear?

Short Answer

Expert verified

a. The gear’s angular acceleration isα=4rad/s2.

b. The tangential acceleration of a tooth on the gear islocalid="1647956044997" at=0.12m/s2.

Step by step solution

01

Given information

We are given with:

diameter=d=6cmradius=r=3cm=0.03mangularvelocity=ω=(2.0+12t2)rad/s

02

Part a) Step 1: Calculation

The gear’s angular acceleration is:

α=dωdtα=ddt(2+12t2)rad/sα=(0+2t2)rad/s2α=trad/s2α=4rad/s2

03

Part b) Step 1:Calculation

The tangential acceleration of a tooth on the gear is:

at=rαat=(0.03m)(4rad/s2)at=0.12m/s2

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