Rotational Kinematics Lab--ZiTong Cheng

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

The linear velocity for points at different radii (3 cm, 8 cm, and 15 cm) is 0.13 m/s, 0.23 m/s, and 0.42 m/s respectively. The direction of the linear velocity is tangent to the circular path, which is the expected behavior in rotational motion.

From these values, the corresponding angular velocities are approximately:

4.33 rad/s at 3 cm

2.88 rad/s at 8 cm

2.80 rad/s at 15 cm

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 created a graph showing how the speed of a point changes with distance from the axis of rotation, using the data: 3 cm → 0.13 m/s, 8 cm → 0.23 m/s, 15 cm → 0.42 m/s. The slope of this graph represents the angular velocity. Based on these points, the angular velocity is relatively consistent across different distances, ranging from about 2.80 rad/s to 4.33 rad/s.

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?

As the radius increases, the acceleration increases as well. This is expected in circular motion where centripetal acceleration depends on both radius and angular velocity. Using the provided data, the angular velocities indicate increasing centripetal acceleration with radius. When graphed, the slope of the acceleration vs. radius graph reflects the square of the angular velocity.

4.How do your results compare to your predictions?

Our prediction was that linear velocity and acceleration would increase with radius, and the data supports this. The angular velocities calculated from the different radii are in a close range, confirming consistent rotational motion throughout.