Physics Chapter 7 Supplementary Apply rotary motion An object that rotates about an internal axis exhibits rotary motion. Angular displacement (denoted as Θ) is measured in terms of rotations or radians. There are 2π radians in one revolution.

Angular Velocity is a measure of the rate of rotation of an object which exhibits rotary motion. Angular velocity ω = ∆Θ ∆t Angular velocity has units of radians per second. Angular velocity can be measured with a stroboscope. Angular acceleration is the rate of change of angular velocity. Angular acceleration a = ∆ω ∆t Angular acceleration has units of radians per second squared.

example A wheel rotates 16 revolutions in 20 seconds. Find its angular velocity.

example A wheel increases its velocity from 12 radians per second to 56 radians per second during a 24 second interval. Find the angular acceleration.

Precession is the rotation of the axis of a rotating object.

All objects exhibiting rotary motion have angular momentum. The momentum of an object depends upon its rotational inertia. The formula for angular momentum is: T(∆t) = I∙ω T = torque (Nm) ∆t = time (s) I = rotational inertia (kg m 2 ) ω = angular velocity (radians/s) Note: The inertia and the velocity vary inversely for a constant momentum. (As the inertia decreases the velocity increases.)

A force of 25 N is applied tangentially to a wheel with a radius of 65 cm for 15 s. The rotational inertia of the wheel is 24 kg m². If the wheel starts from rest, what is its final angular velocity?

The rotational inertia depends upon the objects mass and the distribution of the mass from its axis of rotation. The closer the mass is to the axis, the less inertia the object has. If the disks have the same mass, the disk on the left will roll down an incline faster because it has less inertia.

Demo of conservation of angular momentum T(∆t) = I∙ω What happens to the velocity of a rotating object if its angular inertia is changed?