http://www.ck12.org Chapter 10. Rotational Motion Version 2
- The angular acceleration is not the same as centripetal acceleration, which always points toward the cen-
ter. Angular acceleration is always in the direction or against the direction of angular velocity. The linear
acceleration associated with it points along instantaneous velocity. - Since the mathematics is identical, under constant angular acceleration we can have the big three equations
for circular motion. - Just as linear accelerations are caused by forces, angular accelerations are caused bytorques.
- Torquesproduce angular accelerations, but just as masses resist acceleration (due to inertia), there is an
inertia that opposes angular acceleration. The measure of this inertial resistance depends on the mass, but
more importantly on the distribution of the mass in a given object.Themoment of inertia,I, is the rotational
version of mass.Values for the moment of inertia of common objects are given in problem 2. Torques have
only two directions: those that produce clockwise (CW) and those that produce counterclockwise (CCW)
rotations. The angular acceleration or change in would be in the direction of the torque. - Imagine spinning a fairly heavy disk. To make it spin, you don’t pushtowardsthe disk center– that will
just move it in a straight line. To spin it, you need to push along the side, much like when you spin a
basketball. Thus, thetorqueyou exert on a disk to make it accelerate depends only on the component of the
force perpendicular to the radius of rotation: - Many separate torques can be applied to an object. The angular acceleration produced isαnet=τnetI
- When an object is rolling without slipping this means thatv=rωanda=rα. This is also true in the situation
of a rope on a pulley that is rotating the pulley without slipping. Using this correspondence between linear
and angular speed and acceleration is very useful for solving problems, but is only true if there is no slipping. - Theangular momentumof a spinning object isL=Iω. Torques produce a change in angular momentum with
time:τ=∆∆Lt - Spinning objects have a kinetic energy, given byKrot=^12 Iω^2.