Question

two pulleys with radii 10 inches and 4 inches are connected by a belt. if the smaller pulley rotates at 100 rpm, find the exact values for the angular speed of the other pulley and the linear speed of a point on the belt.

Answer 1

if the smaller pulley rotates at 100 rpm (revolutions per minute) and we know that each revolution is 360 degrees.

this means that every second the pulley does 100/60 = 5/3 revolution

hence radians / pi = 5/3 (degrees / 180)  

radians = pi x 5/3 x 360 / 180 = 10/3 pi radians per second

for the larger pulley, the distance traveled by both pulleys is equal, then

every second, small pulley covers a distance of

d2 = 4pi = 10pi (large pulley circumference) x factor (f)

f = 2/5

then the linear speed of the large pulley = 2/5 x 2pi = 4/3 (10/3 pi) = 40/9 pi = 4.44 rad/sec