Question

The two pulleys have radiis 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.

I got 25pi/18 rad per sec on the bigger pulley and 125pi/48 rad per sec on the smaller one. Are my answers right? Or wrong? Help me pleeeaaase :)

Answer 1

angular velocity is same for bouth

Answer 2

if bouth rotate 25 times in 36 seconds.

Answer 3

@myko only the larger pulley rotates 25 times per 36 sec :)

Answer 4

Do you have a diagram similar to this?
Meaning that the tangential velocity of each pulley is the same?

Answer 5

@kmeds16
Have you solved your problem?

Answer 6

@Mathmate no i don't have, i only have the question lol :)) but i do understand that the velocity (generally) is same for both but they have different angular velocity right because they differ in size? Idk correct me if im wrong haha :)

Answer 7

I did it like this: since v = rw...

v = r1w1 ; v = r2w2
So therefore, r1w1 = r2w2

Answer 8

If the question did not state it, nor having a diagram, then it may be understood in your topic. Anyway,
you would need to use the formula to find the arc length:
\(r_1\theta_1=r_2\theta_2\)
to find the equivalent arc length in a second, so
\(r_1\omega_1=r_2\omega_2\)
would be used for angular velocities.

Answer 9

You have the right formula, just have to solve for \(\omega_2\).

Answer 10

@Mathmate oh, okay :) got it, thank you for the guide! :)

Answer 11

You're very welcome! :)