Rotational Kinematics Lab

Analysis Questions: All Calculations Below

1. Use the velocity components to determine the direction of the velocity vector. Is it in the expected direction? 

The angular velocity from video analysis is 2.75 rad/s. The linear velocity (calculation below) for 6, 12, 18 cm is 0.17 m/s, 0.33 m/s, and 0.50 m/s. The direction of the linear velocity is tangent to the circular path the beam takes which is expected

2. Analyze enough different points in the same video to make a graph of the speed of a point as a function of distance from the axis of rotation. What quantity does the slope of this graph represent?

We used a cosine graph for the fit and the average slope of the three radiii was 2.75 rad/s and this represents the angular velocity. The way we made sure that the value of the angular velocity was the same for the three radii was by using the same video and letting the beam make 2 revolutions.

3. Calculate the acceleration of each point and graph the acceleration as a function of the distance from the axis of rotation. What quantity does the slope of this graph represent? 

Since this is a cosine graph, the slope is still around 2.75 rad/s which is the angular velocity, but the acceleration is incorporated into the amplitude. The centripetal acceleration for radii 6, 12, and 18 cm is 0.45, 0.91, and 1.36 rad/s^2. The tangential acceleration for 6, 12, and 18 cm is 0.03, 0.11, 0.25 m/s^2.

ALL GRAPHS AND EQUATIONS ARE BELOW

Conclusions:

How do your results compare to your predictions?

Our prediction was that the linear velocity and acceleration would increase as the radii increased and this was true based on our data as shown by the calculations below.

6 cm:

12 cm:

18 cm: