Exam 3 Problems

A thin-walled ring and a hollow, thin-shelled sphere, each with mass M and radius r, start from rest at the top of an incline and roll without slipping down to the bottom. Which object has the larger translational velocity at the bottom of the incline?

hollow sphere

if the radius of a satellite orbit doubles, what happens to its period?

increases by a factor of 2.8

You're swinging a ball over your head on the end of a string. If you increase the number of revolutions per minute by a factor of 2, - what happens to the tangential speed of the ball? - the ball increases its angular speed from 12 rad/s to 15 rad/s in 0.75s. What is the angular acceleration of the ball? - how many revolutions does the ball make while it's accelerating?

it doubles

A child hunting for his favorite wooden horsey is running on the ground around the edge of a stationary merry-go-round. The child has a constant angular speed of 0.250 rad/s. His horsey is sitting on the outer edge of the merry-go-round. At the instant the child spots the horsey, one-quarter of a turn away, the merry-go-round begins to move (in the same direction the child is running) with a constant angular acceleration of 0.010 rad/s2. What is the shortest time it takes for the child to catch up with the horse?

- this is quadratic in t, so we solve using the quadratic equation and get 2 solutions t = 7.39 s

A diver decreases her moment of inertia by a factor of 2 in order to complete a triple back flip. What happens to the angular speed of the diver?

she speeds up by a factor of 2

A solid sphere and a hollow sphere, each with mass M and radius r, start from rest at the top of an incline and roll without slipping down to the bottom. Which object has the greater translational velocity at the bottom of the incline?

solid sphere

A ball is tied to the end of a string and is being swung in a horizontal circle at constant speed. What is true about the tangential acceleration?

the tangential acceleration of the ball is 0

Three objects, a disk, a hoop, and a ball, all with radius r=10cm but with masses m(disk)=2kg, m(hoop)=1kg, and m(sphere)=2.5kg, are rolled down a ramp. If all 3 objects start from rest and start at the same position, which one makes it down the ramp first?

all objects reach the bottom at the same time