Lecture 5: Circular Motion - Centrifuges Moving - Reference Frames - Perceived Gravity
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1. Uniform Circular Motion and Centripetal Acceleration:
A particle travels in a circle of radius r with constant speed. The period of one rotation is T (sec); the frequency is f (the number of rotations/sec or Hz), omega is the angular velocity (radians/sec), omega=2pi/T, the speed v= omega*r. The velocity vector is constantly changing direction because of the centripetal acceleration (=v^2/r= omega^2*r). The centripetal acceleration for the rotor of a vacuum cleaner is estimated to be about 400 m/sec^2 which is 40 times larger than g. Note that the centripetal acceleration depends linearly on the radius.
2. There Must be a Pull or a Push:
Sitting on a chair bolted to a fast-rotating turntable, you'll feel a push in your back. Alternatively if you stand on the turntable and you hold onto a post mounted on the table, you will experience a pull in your arms. This pull or push is responsible for the change in velocity (centripetal acceleration).
3. What Happens if there is no Pull or Push?
Your velocity will not change. Thus you move along a straight line with constant speed.
4. Motion of Planets around the Sun:
The gravitational pull provides the centripetal acceleration which is inversely proportional to the distance squared.
5. Swirling Objects Around:
The idea behind a centrifuge and salad spinners.
6. Creating Artificial Gravity via Rotation:
Professor Lewin gives several examples of "perceived" gravity. A space station could rotate such that an astronaut perceives an Earth-like acceleration of 10 m/s^2. However, the direction will be changing all the time!
7. A Centrifuge in Action:
A glass tube filled with a liquid solution with fine particles is spun around in a standard laboratory centrifuge. The acceleration is about 20,000 m/s^2. Thus the particles perceive a "gravitational" force about 2000 times larger than normal, and they "fall" in the direction of this huge "gravitational field". Professor Lewin demonstrates this, mixing NaCl+AgNO_3 => NaNO_3+AgCl; this produces a milky solution. After spinning for a few minutes, the AgCl has precipitated at the end of the glass tube, and the remaining solution has become clear.
8. Swinging a Bucket of Water on a String:
In order to swirl a bucket around in a vertical plane, a centripetal acceleration is required. If you spin fast enough the water will stay in the bucket as the bucket is upside down. To be on the safe side ... bring an umbrella to class!
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