Purpose: The purpose of this lab is to find the conservation of angular momentum about a point that is external to a rolling ball.
Apparatus:
This was the apparatus used to determine the horizontal velocity of the ball.
This is used to find the the conservation of angular momentum about a point external to the ball.
Theory:
When rolling the ball off the ramp and onto the ground, measurements can be made, and kinematics can be used to find the horizontal velocity of the ball, which should be constant as there are no external forces acting on the ball horizontally.
The inertia of the apparatus itself can be determined, using the methods of previous experiments.
The ball is then rolled down the ramp, starting the apparatus. The conservation of angular momentum equation can then be used to find the omega of the ball, which can also be measured experimentally.
Data:
Calculation/Graphs:
The angular acceleration of the apparatus
Calculation of horizontal velocity of the ball
Calculation of the moment of inertia of the apparatus:
Calculation of the theoretical angular velocities:
Analysis:
The radius at which the ball is caught shows that the smaller the radius, the smaller the angular velocity is. The horizontal velocity of the ball affects the initial rotational speed of the apparatus. When we assume the momentum is conserved, the distance at which the ball is caught actually plays a large role.
Conclusion:
The answers we derived theoretically and arrived at experimentally were at a 6.7% and 8.8% error between the 7.6 cm distance and 4.2 cm distance, respectively. Both these errors are within 10%, which is acceptable. Sources of error may be from when the horizontal velocity of the ball is calculated, as we are assuming that it is constant throughout and there are no outside forces acting upon it, when in reality, there is air drag upon it. Error may also be at the apparatus, while measuring the angular velocity and acceleration, as friction plays a part.
Conclusion:
The answers we derived theoretically and arrived at experimentally were at a 6.7% and 8.8% error between the 7.6 cm distance and 4.2 cm distance, respectively. Both these errors are within 10%, which is acceptable. Sources of error may be from when the horizontal velocity of the ball is calculated, as we are assuming that it is constant throughout and there are no outside forces acting upon it, when in reality, there is air drag upon it. Error may also be at the apparatus, while measuring the angular velocity and acceleration, as friction plays a part.
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