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1.) While driving your car you start to wonder about the relationship between th

ID: 1389424 • Letter: 1

Question

1.) While driving your car you start to wonder about the relationship between the car's motion and the rotation of its wheels. At the moment, you are driving on a straight stretch of road at a constant speed of 65 mi/hr. What is the angular velocity for your wheels? You assume that they roll without slipping, and that it's okay to simplify things by thinking of the wheels as disks of radius 9 inches whose mass is evenly distributed. You guess that the mass of one of the wheels is about 15 kg.

2.) How many times do your wheels revolve during a 20 second period while your car's velocity stays constant?

3.) You hit the brakes and stop after 30 seconds. How much torque was applied by the brakes to any one of the wheels?

Explanation / Answer

1)

moment of inertia of disk=0.5mR2

total moment of inertia=4*0.5mR2=2mR2

translational energy is converted into rotational energy

0.5mv2=0.5*2mR2*W2

W=v/sqrt(2)*R

=65*1.6/1.414*9*2.56*0.01

=319.2rad/s

2)

a=28.88/20

=1.44m/s2

s=0.5*1.44*400

=288m

circumference=2*3.14*9*2.56*0.01=1.44

revolutions=288/1.44

=200

3)

torque=IW

intial angular velocity=0

a=104/30 =3.46m/s2

alpha=3.46/9*2.56=0.15rad/s2

W(final)=alpha*t=0.15*30=4.5rad/s

T=2*15*9*2.562*10-4*4.5