Assignment:
1. You are riding your bicycle at constant velocity and you roll enthusiastically through a mud puddle. The bike tires have a radius of 0.31 m and leave a trail of mud coming from the puddle that is 10 meters long in 5 seconds.
a.) What is the angular displacement (angle in radians) one of your wheels went through in this time?
b.) What is the average angular velocity of the tire?
2.) On the first really warm day you go to a playground with some friends and play on the merry-goround. Starting from rest you hold on to the merry-go-round running for 10 seconds and accelerating it with constant acceleration until it reaches a final angular velocity of 2 rad/s.
a.) What is the angular acceleration the merry-go-round undergoes?
b.) What angle in radians does the merry-go-round go through in this time?
3.) After playing basketball you are on your way home and you stop at the top of a hill to tie your shoe. You set the ball down and it starts to roll down the hill. The ball undergoes a constant angular acceleration of 0.1 rad/s2 and has a radius of 0.14 m.
a. What is the angular velocity of the ball after chasing it down the hill for 10 seconds?
b. What angle has rolled through (in radians) during this time?
c. How far down the hill did it roll (arc length)?