Rotation Lab

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

linear velocity: v = rw

4cm: v = 0.051 m/s

8cm: v = 0.102 m/s

12cm: v = 0.152 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?

For the fit, we utilized a cosine graph, and the average slope of the three radii was 1.27 rad/s, which reflects the angular velocity. We used the same video and allowed the beam to make two rotations to ensure that the angular velocity values were the same for all three radii.


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? 

The acceleration increases according to the radius. In circular motion, centripetal acceleration is proportional to both radius and angular velocity. Based on the facts supplied, the angular velocities show that centripetal acceleration increases with radius. When plotted, the slope of the acceleration vs. radius graph equals the square of the angular velocity.


Conclusion

How do your results compare to your predictions? 

We predicted that linear velocity and acceleration would rise with radius, and the evidence confirms this. The angular velocities derived from the various radii are close together, indicating constant rotating motion throughout.


4cm


8cm


12cm



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