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Chapter 4: Q.71 (page 109)

Your 64cmdiameter car tire is rotating at 3.5rev/s when suddenly you press down hard on the accelerator. After traveling 200m, the tire鈥檚 rotation has increased to 6.0rev/s. What was the tire鈥檚 angular acceleration? Give your answer in rad/s2 .

Short Answer

Expert verified

The tire鈥檚 angular acceleration is0.75rad/s2

Step by step solution

01

Given information

Diameter of car tire is D=64cm

Car tire is rotating at 蝇i=initialangularvelocity=3.5rev/s

After traveling d=200m, the tire鈥檚 rotation has increased to 蝇f=finalangularvelocity=6.0rev/s.

We have to find the tire鈥檚 angular acceleration伪 in rad/s2.

02

Formula

Perimeter of circle is 2蟺r

蝇f2=蝇i2+2伪鈭�胃

03

Explanation

By putting values in formula

P=2蟺谤

For radius

r=d2r=642r=32cm

Putting values:

P=2脳3.14脳32cm=200.96cm

Converting the car tire in revolutions:

胃=dP胃=200cm脳100200.96cm胃=99.52rev

For angular acceleration

62=3.52+2伪脳99.52伪=0.1193rev/s2

Now, convert rev/ssin rad/s2

localid="1648908260302" 伪=0.1193rev/ss脳2蟺=0.1193rev/ss脳2脳3.14伪=0.75rad/s2

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