# The Angular Velocity in Belt Drives

Consider the belt drives, the driven pulley: diameter d1, angular velocity w1 and the follow pulley: diameter d2, angular velocity w2.

Assuming that the driven pulley rotate with a constant angular velocity and the belt does not slip on the pulleys, we have w1/w2=d2/d1, so w2 is constant( because w1 is constant).
But I think that the follow pulley will have a torque which is caused by the tensions in the tight and loose sides of the belt. Because of this torque, the follow pulley cant rotate with a constant angular velocity. This is opposite to the above statement ( w2 is constant).
Please explain this misunderstanding for me, thank you.

## Answers and Replies

mfb
Mentor
You have torque (and a tight and loose side) only if the following pulley has friction, and this torque will exactly cancel the frictional torque.

You have torque (and a tight and loose side) only if the following pulley has friction, and this torque will exactly cancel the frictional torque.
But I think, the effect of the belt on the following pulley are the friction forces ( tangent to the pulley) and the press forces ( normal to the pulley). So only friction forces can create the torque on the pulley. That is my thought.

mfb
Mentor
How is that in conflict with my previous post?
If the whole setup is frictionless, both sides will have the same tension. If there is friction, making the pulley slower than the belt or "trying" to slow down the pulley, then you get an accelerating torque from the belt and a braking torque from friction (probably close to the axle).

How is that in conflict with my previous post?
If the whole setup is frictionless, both sides will have the same tension. If there is friction, making the pulley slower than the belt or "trying" to slow down the pulley, then you get an accelerating torque from the belt and a braking torque from friction (probably close to the axle).
yeah, but I wonder that Why the following pulley can rotate with a constant velocity with a torque( due to friction exerted by the belt) ? ( In this case, assuming that the friction between shaft and pulley is negligible ).
Thank you.

mfb
Mentor
( In this case, assuming that the friction between shaft and pulley is negligible ).
If that is true, friction from the belt is negligible as well.

Hi.Daigiaga, sorry but you are forgotten the exterior torques over the two pullies which equals the torques of the belt