Lab 9 - Rotation

Background: If you roll a bouncy ball and a bowling ball down a hill at the same time, which one will reach the bottom of the hill the fastest? If your answer is the bowling ball, then why? Possibly because it is larger and heavier than the bouncy ball, but how do we know that these factors change the speed of each ball at all. Now what if we add in a cylindrical water bottle. How would it compete with the balls? Would the shape make a difference?

When an object is rolling, spinning, or pivoting it is described to be in rotational motion. This concept has a unique set of parameters that is similar in principle to that of linear motion but includes additional variables. More specifically when using the conservation of energy to describe an object's movements, both the object's kinetic energy and its rotational kinetic energy must be considered when the object is rolling. Kinetic energy is described as the energy of an object in motion and defined by the object's mass and velocity. Rotational kinetic energy however, only takes into account the energy of the spinning motion of the object and is defined by the moment of inertia and the angular velocity. The moment of inertia is a measurement of mass and size, and is dependant on the shape of the object in question. For the rolling bouncy ball in the hypothetical situation above, the kinetic energy describes how the object is moving across the space while the rotation kinetic energy is describing the rolling motion of the bouncy ball. 

The purpose of this experiment was to examine how radius, mass, and shape interact with the velocity of an object as it rolls down a ramp to determine which of the three factors influence the results. In order to accomplish this objective, 3 experiments have been developed (1) roll two objects with different radiuses down a ramp, (2) roll two objects with different masses down a ramp, and (3) roll two objects of different shapes down a ramp. 

Equations: 

Moment of Inertia cylindrical shell = I = mr^2

Moment of Inertia solid cylinder = I = 1/2 mr^2

Moment of Inertia sphere = I = 2/5 mr^2

KE = 1/2 mv^2

KE rotational = 1/2 Iw^2

Potential gravitational energy = mgh

Results: 

Experiment 1:

Predicted Result - the two objects will reach the bottom of the ramp at the same time

Observed Result - object 1 with the larger radius reached the bottom of the ramp before object 2

Experiment 2:

Predicted Result - the two objects will reach the bottom of the ramp at the same time

Observed Result - object 1 with the larger mass reached the bottom of the ramp before object 2

Experiment 3:

Predicted Result - the solid cylinder will reach the bottom of the ramp before the cylindrical shell

Observed Result - the solid cylinder reached the bottom of the ramp before the cylindrical shell

Error: In addition to the differences in experiments 1 and 2 discussed above, there was an error made in experiment 2. After the experiment was completed, it was noticed that the objects used in experiment 2 had a different mass but also had a different radius. Given the results of experiment 1, the different radius would not impact the outcome of the trial. However, in order for the experiment to be scientifically reliable, the objects should have had the same radius with a different mass so that only one factor is changing at a time. Even though it was not caught in time for this experiment, future studies should ensure that all control variables are being kept consistent.