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Math Help - RPM of gear

  1. #1
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    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.
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  2. #2
    Grand Panjandrum
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    Quote 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
    Last edited by CaptainBlack; December 23rd 2005 at 10:10 PM.
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