# Circular Motion worksheet

```CIRCULAR MOTION WORKSHEET
1. A yo-yo expert spins the yo-yo around his head in a circle.
The string is 3’ long and it takes 0.8 seconds to go around
him once. How fast is the yo-yo moving?
(Ans: 23.56 fps)
2. How far does it move in each revolution?
(Ans: 18.85’)
3. If the yo-yo weighs &frac14; pound, how much force does he have to exert to keep it going in
the circle at that speed (from question 1)?
(Ans: 1.44 lbs)
4. The vertical loop in a roller coaster is 30m from top to
bottom. What must be the velocity of a 500kg car so that its
occupants feel weightless at the top of the loop?
(Ans: 12.13 m/sec)
5. A group of friends is enjoying a
schoolyard merry-go-round.
It measures 2.5 meters in diameter.
A 40kg girl sits on the edge of it.
The coefficient of friction between
her pants and the floor is 0.3
What is the maximum angular
velocity (in rpm) that the girl can
be spinning at, and still stay on (if
she doesn’t hold on to the rails)?
(Ans: 14.65 rpm)
6. If the spin rate was increased to 20 rpm, the girl would have to sit closer to the center
of the ride to avoid flying off. Where would she have to sit (measured from the center)?
(Ans: 0.671m)
7. From her new location, she notices that she left her backpack where she was originally
sitting (i.e. at the edge of the ride) and it hasn’t flown off yet. What must be the
minimum coefficient of friction between the pack and the floor?
(Ans:  = 0.559)
8. If it did suddenly fly off, at what speed would it go? (Ans: 2.618 m/sec)
```