Lab 6: Uniform Circular Motion
Name: __________________________
Goals:
- Use circular motion physics to measure the mass of a rubber stopper.
Centripetal acceleration:
When an object moves with a constant speed v in a circle of constant radius r , we say that the object is in uniform circular
motion. An object in uniform circular motion does not have a constant velocity, because the direction of the velocity is changing
all the time. If the velocity is not constant, the object must be accelerating. As it turns out, the object is accelerating toward the
center of its circular path at all times, and the magnitude of the acceleration is given by
acentripetal 
v2
.
r
Solving UCM problems:
When an object is in uniform circular motion, you can use the speed and the radius of curvature to infer the force acting on the
object:
F  ma  Fcentripetal  macentripetal  m
v2
r
Now that you know the force on the object, you have to figure out what is actually causing the force physically (in the case of
this lab, it’s the tension in a string).
Period and speed:
It is often easier to measure the period of an object in UCM than it is to measure the speed. These two quantities are easily
related by thinking about one revolution of the object. During one revolution, the object travels a distance of 2 r in a time of
one period (T). Therefore, the speed is given by:
v
2 r
.
T
1. Set up the uniform circular motion experiment as shown below. The stopper is twirled around on a horizontal circular
path while the tension in the string holds up a 1 kg mass. After a few trial runs, you should decide on a radius around
50-80 cm and mark it on the string using a sharpie.
radius of curvature
rubber stopper (mass unknown)
pen body
1 kg
Radius of curvature: ___________ m
2. Now twirl the stopper over your head in uniform circular motion. Have one group member take the time for 20
revolutions in order to measure the period:
Time for 20 periods: __________ s
Time for one period: __________ s
3. Draw all force vectors into the diagram for the stopper and the hanging mass. Keep everything symbolic for now –
using M and m for the masses.
m
M
4. Apply Newton’s second law Fnet ma to each object, and write down each corresponding equation. You can use FT
for the tension, since we have already used T for period. The equations should be written entirely in terms of FT , T ,
m , M , g and R .
Equation for the hanging mass: _____________________
Equation for the stopper: ______________________
5. Eliminate tension from the system of equations, then solve for the mass of the stopper in terms of T , m , M , g and R
Show your work carefully:
m = __________________
6. Plug in all the necessary numbers and compute the mass of the stopper
Mass of stopper (from UCM experiment) =
___________ g
Mass of stopper (measured on a scale) =
___________ g
Percent difference:
mUCM  mscale
 100  _________ %
mscale