ANGULAR SPEED

Question

A two-inch-diameter pulley on
an electric motor that runs at 1700 revolutions per
minute is connected by a belt to a four-inch-diameter
pulley on a saw arbor.
(a) Find the angular speed (in radians per minute) of
each pulley.
(b) Find the revolutions per minute of the saw.

Answer 1

Step 1:

(a)

Revolutions per minute of 2-inch diameter pulley is 1700.

Angular speed  .

Where, Angle generated by pulley.

Angular speed of 2-inch diameter pulley .

Angle generated by 2-inch diameter pulley.

.

Angular speed of 2-inch diameter pulley is .

Step 2:

Angular speed of 4-inch diameter pulley .       (Since )

Radius of 2-inch diameter pulley .

Radius of 4-inch diameter pulley .

Substitute corresponding values in .

.

Angular speed of 4-inch diameter pulley is .

Step 3:

(b)

Angular speed of saw arbor is .

Revolutions per minute of the saw is 850.

Solution:

(a) Angular speed of 2-inch diameter pulley is .

     Angular speed of 4-inch diameter pulley is .

(b) Revolutions per minute of the saw is 850.