PHYS4A/ Fall 2014; Conservation of Linear and Angular Momentum

Purpose: Prof. Wolf does an experiment to show that linear and rotational momentum are both conserved.

In this experiment, Prof Wolf performs an experiment while the rest of us observed and made calculations. For the first part of the experiment, a ball rolls down a ramp and we are asked to calculate the rolling velocity of the ball and the launch velocity of the ball under constant acceleration and through slipping. Calculations below show that with the static friction causing the ball to roll, launch velocity was slightly higher.

Velocity calculations

Angular acceleration was measured by Wolf as we were doing calculations

Once the velocity was calculated, the moment of inertia had to be calculated using the same method as the previous lab with moment of inertia. This was needed so that conservation of momentum could be used in the next part as it would be an inelastic collision and energy would not be conserved. Since Prof. Wolf had already attached a hanging mass to the disks and run the experiment to find angular acceleration, all we had to do was use that and Newton's second law to find the moment of inertia like below.

Moment of inertia of the disks calculations

Prof. Wolf and the lab set-up

Prof. Wolf then ran the experiment to make better use of time as we waited for groups to get their values. The ball was released from the top of the ramp and the ball was launched into a metal trap on the spinning disk which then started to spin due to rotational momentum being transferred into the disk.

Calculations for omega

 Once the experiment was over, using conservation of momentum, we were able to calculate a theoretical omega value once the collision occurs. This omega value was then compared to the graph below where the position in radii was recorded vs time. The slope of this graph was the angular velocity of the spinning disk and the value of 1.775 rad/s was compared to our calculated value of 1.95 rad/s.

The values were fairly close and shows that momentum was conserved throughout the experiment since we were able to use the conservation to calculate what we needed for the final goal.