The purpose of this experiment was to investigate the motion of an object in a circular path with constant speed. Uniform circular motion is achieved when an object is moving in a circular path while turning through equal angles in equal time intervals, or with constant angular velocity. In this form of motion, the angular velocity and the angular acceleration of the object change in direction but do not change in magnitude. Because the direction is changing, there must be a force acting on the object; in the case of uniform circular motion, this force (also referred to as the centripetal force) is directed towards the center of the circular path. Using a rotating mass apparatus attached to a force sensor, this experiment studies Newton’s Second Law of Motion applied to uniform circular motion.
II. Data and Analysis
Average Force with Varying Mass
Av speed (m/s)
Av Force (N)
Theory force (N)
Mass (kg)
2.342
0.467
0.48
0.005
2.393
0.789
0.78
0.01
2.398
1.029
1.07
0.015
2.384
1.348
1.34
0.02
2.396
1.66
1.64
0.025
2.372
1.942
1.88
0.03
The two graphs above show the varying velocity (squared) of the object in motion versus the experimentally determined average force and theoretical force, respectively. The slope of the linear regression model of the experimental data is equal to 0.3096, which differs from the slope of the graph of the theoretical data, which is equal to 0.3356, by about 7.75%. Again using equation 1.9, the uncertainty in our slope and our intercept were determined to be
