Relationship between tangential and angular properties.
Pre-requisite skills: Basic vector algebra, reference frames.
Approximate completion time: 30 minutes.
Provide sufficient detail to verify that the assignment was completed in a meaningful manner.
MERLOT site: Rotational Motion with Friction, by Angel Franco Garcia. (direct link).
Applet by Angel Franco Garcia
In this applet, the circular wheel is partitioned into six equal segments. The radius of the wheel is initially set to 1.0 meters.
A. Preliminary Investigation
What is the circumference, C? What is the arc length S of each section in SI units?
B. Rolling Without Slipping
With r = 1.0 m, set both the linear velocity to 2 m/s and the angular velocity to 2 rad/sec.
1. How long will it take for the wheel to complete one revolution? By watching the clock in the upper right of the applet, verify your answer.
2. The tic marks on the level surface are purposely drawn to be the same distance apart as the tic marks on the wheel (in other words, they are a distance S apart). How far horizontally does the wheel travel in the same time as it takes to complete one revolution? Compare this distance to the circumference C. How are they related?
C. Rolling With Slipping
1. Change the linear velocity to 1 m/s and press the Start (Empiaza) button. After one revolution, how does the horizontal distance traveled by the wheel compare to its circumference?
2. Now change the linear velocity back to 2 m/s, but change the rotational velocity to 1 rad/s. Press Start, and answer the same question as above (Question B-1).
D. General Considerations
From your previous answers in Parts B and C, can you describe one fundamental characteristic of rolling without slipping?
Helpful Resources
- Rolling without Slipping by B. Surendranath Reddy
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