The angular velocity of a particle traveling on a circular path is the ratio of the angle traversed to the
amount of time it takes to traverse that angle.
1. Consider the Earth which rotates on its axis once every 24 hours. Find the angular velocity of a
person ( point) on the earth after 24 hrs.
2. A second example is that of a ceiling fan. If the fan rotates 30 times per minute what is the angular
velocity of a fly on the end of a blade of the ceiling fan in degrees per hour?
We will now calculate the linear velocity of a point on the surface of the Earth and a point on the tip of a
fan blade.
1. The radius of the Earth is approximately 4000 miles. Find the linear velocity of a person on the
surface of the earth after 24 hours.
2. To calculate the linear velocity of the fan blade, we note that the blade rotates 30 times in one minute.
Find the linear velocity of a fly on the blade of the fan in miles per hour.
Let's Practice:
1. A Ferris Wheel rotates 3 times each minute. The passengers sit in seats that are 25 feet from the
center of the wheel. What is the angular velocity of the wheel in degrees per minute and radians
per minute? What is the linear velocity of the passengers in the seats?
2. Assume the hard drive on a computer is circular and rotates at 7200 revolutions per minute. What
is the angular velocity in radians per minute? What is the linear velocity in inches per minute of a
particle located 2 inches from the center of the hard drive? …. in miles per hour?