Lecture 19: Rotating Rigid Bodies - Moment of Inertia - Parallel Axis and Perpendicular Axis Theorem - Rotational Kinetic Energy - Fly Wheels - Neutron Stars - Pulsars
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1. Angular Acceleration in Circular Motion:
An object in circular motion can experience a tangential acceleration (resulting in a change of its speed). Similarities between equations for linear motion and rotational motion are drawn.
2. Kinetic Energy of Rotation - Moments of Inertia:
The kinetic energy of rotation of a disk is derived and related to its moment of inertia and angular velocity. The moment of inertia depends upon the shape and mass of an object; it differs for different axes of rotation.
3. Parallel Axis and Perpendicular Axis Theorems:
The Parallel Axis theorem is very useful for calculating the moment of inertia about an axis offset from the center of mass. The Perpendicular Axis theorem is useful for thin objects.
4. Energy Management with Flywheels:
A scenario is explored where the potential energy of a car coming down a mountain is stored in a flywheel (while stepping on the brakes) rather than dissipated into heat. The rotational kinetic energy of the flywheel can, in principle, at a later time be used to increase the car's speed when needed. A demonstration shows how rotational energy in a flywheel gets converted into linear motion of a toy car.
5. Flywheels at MIT's Magnet Lab:
A pair of very massive flywheels rotating at 6 Hz are used to convert rotational kinetic energy into magnetic energy and vice versa for energy storage.
6. Rotational KE in Planets and Stars:
The rotational kinetic energy of the sun and Earth due to their spin are presented, along with data from the Crab pulsar. The Crab pulsar, with a spin period of 33 ms, is spinning down; its spin period is increasing by 36.4 nanoseconds/day. The radiated power (in the form of radio waves, light, X-rays and gamma-rays) results in a loss of rotational kinetic energy. In other words, rotational KE is converted to electromagnetic radiation.
7. Slides of MIT's Flywheel and the Crab Nebula:
Slides are shown of the Flywheels in MIT's Magnet Lab, and of the Crab Nebula (home of the Crab Pulsar). Stroboscopic pictures show that the Crab Pulsar blinks on and off in optical light as it rotates about its spin axis. An X-ray image of the Crab Nebula made with the Chandra Observatory is also shown.
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