Finding Linear Velocity

Examples:

Find the linear velocity of a point on the edge of a lawn mower blade 18 inches long evolving at 300 rpm. Find in inches per minute.

v = 300 rev / 1 min * 2Pi / 1 rev * 18 in / 1 * 1 min / 60 sec = 10800 / 60 = 180Pi inches per second

A point is 25 inches from the center of a circle. If the circle is rotating at 15 rev per sec, find the velocity of the point in feet per minute.

v = wr = 1800 Pi rad / 1 min * 24 in / 1 * 1 ft / 12 in = 3600 Pi ft / min

A point on the rim of a tir is 14 inches from the hub of the wheel. If the wheel is rotating at 120 rpm, find the linear velocity of the point in inches per second.

v = 120 rev / 1 min * 2 Pi / 1 rev * 1 min / 60 sec * 14 in / 1= 56 Pi in /sec

A point on the edge of a gear 8 inches in diameter is revolving at 180 rpm. Find the linear velocity of this point in inches per second

v = 130 rev / min * 3 pi / 1 rev * 1 min / 60 sec * 4 in / 1 = 24 Pi in / sec

A person on the end of a skating whip is 10 feet from the center person. If they want to make 20 revolutions per minute, how fast will the last person in the line have to skate?

v = 20 ev / sec * 2 Pi / 1 rev * 10 ft / 1 = 400 ft/ min

Find the angular velocity in radians per minute and the linear velocity in feet per minute of the point on the rim of a wheel with 32 inch diameter rotating at 5 rev/sec.

w = 5 rev / 1 sec * 2 Pi / 1 rev * 60 sec / 1 min = 100 Pi rad/min

v = 600Pi / 1 min * 16 in * 1 ft/ 12 in = 800 Pi ft / min

Note: In the above equation, Pi is the symbol pi and the operations of division indicate fractions.