# Advantage of using a bigger pulley in belt drive?

1. Apr 17, 2013

### hihiip201

Hi :

lets examine the following scenario

1.

M --------- o where M is a mass, o is a pulley with it's outter radius r attached to a mass by the belt drive -------. frictionless.

2.

M ---------O same setup but the radius is now bigger, R.

I was reading somewhere saying, a smaller pulley can move things quicker, so i decided to derive this to see for myself.

the following is the result:

for case 1:

alpha = T/(J+Mr^2)

case 2:

alpha = T/(J+MR^2)

in other word, for the same torque generated from DC motor, alpha is higher for case 1.

also, in the case where the pulley rotates at a constant velocity, constant torque output, case 1 amplify the force on the mass M where as the force on the Mass M in case 2 would be lower.

so my question is, why would anyone choose case 2 at all? what advantage does it have on any applications?

thanks

2. Apr 17, 2013

### CWatters

In this contect "constant velocity" means "constant angular velocity". So with the smaller pulley the force available to accelerate the object will be greater but the linear velocity of the belt will be lower.

Changing r is like changing gear on your car.

3. Apr 17, 2013

### hihiip201

but wouldn't the mass still be able to moved quicker though since for a constant T the force on the mass would be higher?

I know this is related to how if you rotate a disk from its side you apply less force but cover more distance, vice versa, but i don't know how to apply that principle in this case.

4. Apr 17, 2013

### CWatters

When you say "moved" you need to be clear if you mean "moved at a constant velocity" or "accelerated"?

If the system is frictionless and the mass is moving horizontally it takes no power (no torque) to move the mass at a constant velocity. The maximum velocity will depend on the motors angular velocity and the gearing. The radius r is part of the gearing.

If you are accelerating the mass or raising it up an incline then that's a different matter.