Rotational Kinematics - Spinning Beam

Data From Video Analysis

5cm

10cm

15cm

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

 

The angular velocity (w) from the video analysis data is close to a constant. The average linear velocities for 5, 10, and 15cm are 0.36 m/s, 0.7 m/s, and 1.02 m/s respectively. These velocities are tangent to the circular path the beam travels, which is the expected direction for the linear velocity components in a circular motion.

 

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 the graph represent?

 

We analyzed 3 different points on the beam in the same video and did video analysis on them by fitting the curve with the cosine graph. After that we plotted speed values we got against radius. The slope of this graph corresponds to the angular velocity (w), which is constant in all radii. This agrees with the expectation of v=wr.

 

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

 

We calculated the centripetal acceleration for each measurement using the formula: a=(v^2)/r. When we plotted the graph of acceleration-radius, we saw that the curve was quadratic which agrees with the formula: a=(w^2)r. These show that the slope of this graph shows (w^2).

 

Conclusion

Our results shows that linear speed increases linearly with the radius and centripetal acceleration increases quadratically. This agrees with the predicted physical relationships (v = wr and a = (w^2)r).