Angular Velocity

Question

8. Two pulleys are connected by a belt. The smaller pulley has a diameter of 8 cm and the larger pulley has a diameter of 12 cm. The smaller pulley is rotating at the rate of 60 rpm.

 

a. Find the angular velocity of each pulley in radians per second. Express the answer in terms of pi

 

b. Find the velocity of a point on the rim of each pulley in cm. per second..9. Two pulleys have a radii of 15 cm and 8 cm respectively. The larger pulley rotates 25 times in 36 seconds. Find the angular speed of each pulley in radians per second. Express your answer in terms of pi

Answer 1

question 8

 

for the smaller pulley, it does 60 rpm (revolutions per minute) each revolution is 360 degrees. this means that every second the pulley does 1 revolution (i.e. 360 degrees)

radians / pi = degrees / 180  

radians = pi x 360 / 180 = 2 pi radians per second

 

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

then d1 = d2

every second, small pulley covers a distance of 8pi (small pulley circumference) = d1

d2 = 8pi = 12pi (large pulley circumference) x factor (f)

f = 2/3

then speed of the large pulley = 2/3 x 2pi = 4/3 pi = 1.33 rad/sec

 

question 9 is similar

large pulley speed = 1.389 rad/sec

small pulley speed = 2.604 rad/sec