Thread: RPM of gear

I have a steal gear with a radius of 3 inches that ways 3lbs. I am going to apply 1.5 foot pounds (2.04Joules) of torque to the gear for .5 seconds. What formula can I use to figure the RPMs of the gear? Thanks for the help.

Originally Posted by Greg E

I have a steal gear with a radius of 3 inches that ways 3lbs. I am going to apply 1.5 foot pounds (2.04Joules) of torque to the gear for .5 seconds. What formula can I use to figure the RPMs of the gear? Thanks for the help.

We have torque is equal to angular acceleration times the momemt of inertia:

,

where we are working with a set of consistent units. Since it is about 40 years since I used Imperial/Customary units I will convert all units to SI. The mass of your grear is , and the radius of the gear is . We will treat the gear as a disk and assume that the moment of inertia we require is that about its axis so:



So assume a constant torque of is applied for then this results in an angular velocity of:



RonL