http://www.ck12.org Chapter 8. Angular Motion and Statics
8.1 Angular Momentum
Objectives
The student will:
- Understand what is meant by a rigid body
- Understand what torque is and how to use it in solving problems
Vocabulary
- angular momentum:The product of rotational inertia and angular velocity.
- angular velocity:How quickly an object is turning.
- axis of rotation:The center around which an object turns, which might or might not be outside of the object.
- radian:The distance around the edge of a circle of radius 1.
- revolution:An object turning around a center that may or may not be outside of the object.
- rotation:An object turning without moving its center of mass, like a spinning top.
- rotational inertia:The difficult required to turn an object.
Introduction
Besides moving through space in a given direction, a solid object can spin or turn. This requires new measures of
motion beyond position, velocity, and acceleration –as well as some new terminology. Starting with the new terms:
- Rotationmeans an object turning without moving its center of mass, like a spinning top.
- Revolutionmeans an object turning around a center (oraxis) that might or might not be outside of the object.
So what makes an object more difficult to turn? The difficulty it requires to push an object through space is called
inertia or more precisely translational inertia. Inertia is equal to mass. The dificulty required to turn an object is
calledrotational inertiaor sometimes “moment of inertia”. This is symbolized by the letterI(for inertia).
Try this out. Take a long object like a broomstick or baseball bat. Lay it flat and try to spin it with one hand. This
can be difficult. Now instead, stand it upright and just give a twist with your fingers to turn it around. The same
object is more difficult to spin one way than the other. Rotational inertia depends on both the mass and the mass
distribution of an object. Mass closer to the axis is easier to turn. Mass farther from the axis is harder to turn.
Angular velocityis defined as how quickly an object is turning, and is symbolized by the Greek letter omega:ω. In
physics, angular velocity is generally measured in one of two units:
- Revolutions per second, or rev/s. A complete rotation or revolution is equivalent to motion through 360-
degrees. An object that turns around 30 times in one minute has an angular velocity of 0.5 rev/s. - Radians per second or rad/s. Aradianis the distance around the edge of a circle of radius 1. It takes 2π
radians to complete one circle, so 2π−radians are equivalent to 1 revolution (360 degrees).
Click the following link for a demonstration: http://demonstrations.wolfram.com/AngularVelocityOfACompactD
isc/.