Physics 8: 4-6 Rotational Dynamics
Text Reading: Giancoli, Physics - Principles with Applications, Chapter 8: 4-6
- 8.4: Torque (symbol Greek letter tau: τ) is force acting on an object along some line other than one passing through the center of mass, causing the mass to spin. We calculate torque as the cross product F̅ x r̅ of the radius vector (displacement from the radius) and the force vector. The magnitude of the torque vector is τ = rF*sin θ. The direction of the torque is given by the right hand rule. Notice that if r = 0 (the force passes through the center of mass), τ = 0, the object does not spin, and all motion is translational.
- 8.5: Since we have a force, we have to have a relationship between force, mass, and acceleration resulting in a law of rotational inertia. The problem is that not all parts of a spinning object have the same distance r̅ from the center of rotation. However, we can sum up the inertal "moments" of individual mass bits and determine a moment of inertia for the rotating object, similar to the center of mass for translational motion. For known shapes and their moments, we can calculate the torque, inertia, acceleration, and other characteristics as if the spread-out inertial pieces were concentrated at one point.
- 8.6: Once we understand that we need to use the moment of inertia I as a kind of mass-at-position substitute, we can calculate torque = inertia * acceleration, τ = Iα, using known moments.
(from chapter 2)
|F = ma
||τ = Iα
Read the following weblecture before chat: Inertia, Acceleration, and Force
Use the physics simulation ==>HERE<==
to experiment with objects rolling and sliding down an inclined plane.
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