## Effect of a force on angular velocity?

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sgfw
Posts: 46
Joined: Wed Jun 19, 2013 11:47 pm UTC

### Effect of a force on angular velocity?

I'm in a physics class, and I have learned that if a force is applied to an object on the center of mass, then the object does not spin, but if a force is applied to another part of the object, then it will spin. How do you calculate how a force would affect an object both rotationally and directly?

cyanyoshi
Posts: 409
Joined: Thu Sep 23, 2010 3:30 am UTC

### Re: Effect of a force on angular velocity?

Just like an object has a total mass that relates velocity to momentum, the distribution of its mass gives it rotational inertia (called moment of inertia) that relates angular velocity to angular momentum. The sum of the applied torques about an object's center of mass is then equal to the rate of change of the angular momentum, which is just the rotational version of Newton's 2nd law.

Mokele
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Location: Atlanta, GA

### Re: Effect of a force on angular velocity?

An off-axis force will result in both simultaneous rotation and linear acceleration - if you poke a pen in zero G, it'll spin while drifting away from you.

You can, however, decompose it. If you see an object with both linear and rotational acceleration, you can calculate the force applied to the CoM and a "free moment", an opposing force couple that produces a pure rotation. It's often used in inverse dynamics for studying kinetics of robot or animal movement.
"With malleus aforethought, mammals got an earful of their ancestor's jaw" - J. Burns, Biograffiti

sgfw
Posts: 46
Joined: Wed Jun 19, 2013 11:47 pm UTC

### Re: Effect of a force on angular velocity?

Mokele wrote:You can, however, decompose it. If you see an object with both linear and rotational acceleration, you can calculate the force applied to the CoM and a "free moment", an opposing force couple that produces a pure rotation. It's often used in inverse dynamics for studying kinetics of robot or animal movement.

So to do this, would you find the portion of the force vector that faces the center of mass, and use that for linear acceleration, and then use everything else for rotational?

Flumble
Yes Man
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### Re: Effect of a force on angular velocity?

As far as I understand it now, you apply the force linearly as usual, a=F/m (it never matters where forces are applied) and you apply the force rotationally as alpha=Fxr/I. (cross product of force and vector to the center of mass divided by the (second?) moment of inertia)

If this gives you a headache like it gave me, see this topic: https://www.physicsforums.com/threads/a ... on.623383/

cyanyoshi
Posts: 409
Joined: Thu Sep 23, 2010 3:30 am UTC

### Re: Effect of a force on angular velocity?

Right. It doesn't matter where the forces are applied, whether it's through the center of mass or not. The sum of forces is still equal to mass times the acceleration of the center of mass. You can then deal with change in orientation on its own by looking at the net torque due to these outside forces.

The actual rotational equations of motion are usually hard to solve, though. If you are interested, Euler's equations are good in practice for looking at how angular velocity of a rigid body is affected by applied torques/moments, but they only work for a body-fixed reference frame.