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PIESampleRotationProbs

Show all work & draw large, neat diagrams.

Out-of-control Ferris Wheel

A 30 meter tall Ferris wheel is spinning wildly out of control clockwise at a speed of 10 RPM (picture what 10 RPM looks like in your mind--it doesn't appear to be that fast). Unfortunately you are sitting in a hanging bucket on the Ferris wheel. Feel free to use any units you like, as long as your final answers also include units that any average person could understand.

Picobonus: What college did Mr. Ferris attend and in what year did he invent the Ferris wheel?

1. What is your speed? (angular and tangential)

2. What is your centripetal acceleration?

Bonus: What is the difference between centripetal and centrifugal acceleration? Give definitions for both and then demonstrate the concepts for this problem and the problem below.

3. Find you apparent weight (express as a weight and in g-forces) and the direction of that apparent weight when you are at the following positions:

4. If the bucket fell off at the 10 o'clock position, where and when would it land, and with what speed? Answer this question using TWO methods (energy and freefall). Do both methods yield satisfactory results? Do the results match?

Satellite Orbits, etc. ...

Suppose you found a clever way to find the distance to the moon (laser rangefinder??). One other common fact you should know is the rotational speed of the moon as it orbits the earth (you should know this in everyday units of measure). If that orbital altitude is 225,000 miles, and you know the mass of the earth is 5.98 x 10⁶ kg, find...

5. ...the speed of the moon (rotational and tangential) based on your common knowledge of the rate at which the moon orbits the earth.

6. ...the mass of the moon.

7. Suppose you climb into your space suit and use your ACME teleportation machine to transport yourself to a point in space that is 225,000 miles from the surface of the earth (assume the moon is on the opposite side of the earth from your position). Relative to the normal pull of gravity you feel on the earth's surface, how much gravitiational acceleration do you feel? (i.e., g-force)

8. What will happen to you once you teleport to the point in space (will you float, move, feel heavy, feel light, etc.)

9. How much additional g-forces do you feel from the moon (remember, it is on the opposite side of the eart from your position.

Missing concepts...

10. You'll notice that the only concept we left of of this practice test is spring energy. Can you think of a clever way to incorporate a spring into the first problem?