A tetherball is attached to a pole with a 2.0-m rope.It is circling at 0.20 rev/s.As the rope wraps around the pole,it shortens.How long is the rope when the ball is moving at 6.0 m/s?
A)1.8 m
B)0.83 m
C)1.2 m
D)1.0 m

Question

Quizplus · Accepted Answer

The speed of the ball can be calculated using the formula v=2πr/T, where v is the speed, r is the length of the rope, and T is the period (time for one revolution). 
0.20 rev/s means T=1/0.20=5 s. 
v=2π(2.0)=4π m/s 
Now, we can use the conservation of angular momentum to find the length of the rope at a given speed. Since the angular momentum of the system is conserved, we can write: 
L=Iω=Iω', 
where L is the angular momentum, I is the moment of inertia (for a point mass, I=mr^2), ω is the initial angular frequency (ω=2π/T), and ω' is the final angular frequency (ω'=v/r). 
Solving for r, we get: 
r=v/ω'=v/(2π/T)=vT/(2π)=6.0 m/s x 5 s/(2π)=0.83 m.

A Tetherball Is Attached to a Pole with a 2