v = w * r

where:

v = linear speed

w = angular velocity

r = radius

1. A spindle is rotating at 1800 rpm (revolutions per minute). What is the linear speed of a point that is 20 inches from the center?

1. A spindle is rotating at 1800 rpm (revolutions per minute). What is the linear speed of a point that is 20 inches from the center?

given:

r = 20 in

w = 1800 rev/min * 2 pi/rev * 1 min/60 sec

w = 1800 * 2 * 3.1416/60

w = 188.4 rad/sec

find:

v = linear speed of a point 20 in from center

solution:

v = w * r

v = 188.4 rad/sec * 20 in

v = 3768 in/sec

converting to fps,

v = 3768 in/sec * 1 ft/12 in

v = 3768/12

v = 314 fps (feet/sec)

**2. A belt with 800 in/min speed turns a 24-inch diameter pulley. Compute the angular velocity of the pulley.**

given:

v = 800 in/min (ipm)

r = 24/2

r = 12 in

find:

w = angular velocity of the pulley

solution:

v = w * r

800 = w * 12

w = 800/12

w = 66.67 radians/minute

converting to revolutions per minute (rpm),

w = 66.67 rad/min * 1 rev/(2 * pi) rad

w = 66.67/(2 * 3.1416)

w = 10.6 rev/min (rpm)

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