# Pulleys

## An Application of Angular and Linear Velocity

In the following math applet, change the radius of each pulley and observe the effect on the linear velocity of the belt and the angular velocity of each pulley. Click the "Start" button to begin the animation.

Observe that:

• The smaller pulley has the higher angular velocity; and
• The linear velocity for the outer edge of both the 2 wheels is the same. (It has to be, or the belt would break).

Also, notice that the ratio of the angular velocities is the inverse of the ratio of the radius of the two pulleys. For example, if r_1=5 and r_2=2 (ratio 5/2), the ratio of the angular velocities is 1.2/3 = 2/5.

### Units

In the following applet, the units are as follows:

• The radius is in meters.
• The angular velocity is in radians/sec.
• The linear velocity is in meters/second.

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