Peoples Physics Concepts

http://www.ck12.org Chapter 9. Rotational Motion

Guidance

These equations work in the case of constant angular acceleration. Use them just as you would use the linear

kinematic equations studied in the One-Dimensional Motion lessons. Just replace displacement with the change in

angle, the velocity with the angular velocity and the acceleration with the angular acceleration.

• When something rotates in a circle, it moves through aposition angleθthat runs from 0 to 2πradians and
  starts over again at 0. The physical distance it moves is called thepath length.If the radius of the circle is
  larger, the path length traveled is longer.


• The angular velocityωtells you how quickly the angleθchanges. In more formal language, the rate of change
  ofθ, the angular position, is called the angular velocityω. The direction of angular velocity is either clockwise
  or counterclockwise. Analogously, the rate of change ofωis the angular accelerationα.


• The linear velocity and linear acceleration of rotating object also depend on the radius of rotation, which is
  called themoment arm(See figure below.) If something is rotating at a constant angular velocity, it moves
  more quickly if it is farther from the center of rotation. For instance, people at the Earth’s equator are moving
  faster than people at northern latitudes, even though their day is still 24 hours long –this is because they have
  a greater circumference to travel in the same amount of time.

Example 1

A 2 kg mass is attached to a .5 m long string. Starting from rest, the mass is given a constant angular acceleration of
2 rad/s^2. If the string breaks when the tension exceeds 50 N, how long will it be before the string breaks and what
will the object’s angular displacement be?

Solution

To start, we first want to find the object’s linear speed when the string breaks.