# Math Help - RPM of gear

1. ## 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.

2. 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:

$\tau=I\cdot \alpha$,

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 $\approx 1.36\ kg$, and the radius of the gear is $\approx 0.076\ m$. We will treat the gear as a disk and assume that the moment of inertia we require is that about its axis so:

$I=\frac{1}{2}m\cdot R^2 \approx 0.0039 \ kg.m^2$

So assume a constant torque of $2.04\ Joules$ is applied for $0.5 \ s$ then this results in an angular velocity of:

$\approx \frac{2.04}{0.0039}\cdot 0.5 \approx 262 \ rad/s \sim 2500\ rpm$

RonL