# Relationship between radius and force under constant torque?

1. Jul 19, 2015

### 24forChromium

Suppose that there's a wheel. A constant torque is applied to the wheel from the central axis.

What is the relationship between the amount of force received by each particle on the wheel in relation to the distance each particle is away from the axis?

2. Jul 19, 2015

### brainpushups

By 'amount of force' do you mean the total tangential force? Of course, as the object increases its angular speed the centripetal component will grow. Assuming a rigid body model the tangential force increases linearly from the axis of rotation.

3. Jul 19, 2015

### 24forChromium

you mean:

4. Jul 19, 2015

### brainpushups

Sorry if I wasn't clear. Say you have a force F applied at the radius R. The tangential force on a particle at a distance R/2 will be F/2 (again, assuming a rigid body model).

5. Jul 19, 2015

### 24forChromium

I see, and I suppose it doesn't matter whether or not is the torque applied from the center or from the side?

6. Jul 19, 2015

### brainpushups

I don't believe it does. Think about what is happening in the wheel. The points on the edge speed up with a tangential acceleration which must be proportional to the tangential force. Because the tangential acceleration varies linearly from the pivot the tangential force must also.

7. Jul 19, 2015

### 24forChromium

that sounds right, and the points further away from the axis have a greater moment of inertia don't they? If they have a greater angular inertia and have to reach an angular velocity higher than those near the axis, shouldn't the equation be F = T*r^2 ?

8. Jul 19, 2015

### brainpushups

Yes.

The particles have the same angular velocity in the rigid body model.

Not sure how you reason that.

9. Jul 21, 2015

### jbriggs444

If the body is rigid then all points attain the same angular velocity and have the same angular acceleration.

10. Jul 23, 2015

### Let'sthink

I think only certain, I will say, physics grammar need to be observed while asking or replying questions. I point out some instances:
1. Force cannot be given or accepted like energy. It acts on an object, which should be a material having some mass, I think. in that sense the phrase force at a point has no significance, if we do not know ultimately it is acting on what. In this case where-ever we apply the force it is acting on the whole wheel.
2. moment of Inertia of a point with no regard to its mass is again a meaningless statement.

11. Jul 23, 2015

### tommyxu3

That may depend on where you observe.