# The Forces of Rolling

## Homework Statement

A constant horizontal force app of magnitude 15 N is applied to a wheel of mass 8.9 kg and radius 0.39 m. The wheel rolls smoothly on the horizontal surface, and the acceleration of its center of mass has magnitude 0.76 m/s2. (a) What is the magnitude of the frictional force on the wheel? (b) What is the rotational inertia of the wheel about the rotation axis through its center of mass?

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## The Attempt at a Solution

I don't even know where to begin for either part. For (b) I tried using several rotational inertia equations; however, none of the ones I used worked.

LowlyPion
Homework Helper
The way it's described what is the force going into?

There is translational acceleration of the center of mass horizontally.

But what else is accelerating?

The horizontal force would be going into the wheel in order to make it move and the wheel itself would be accelerating? Maybe?

LowlyPion
Homework Helper
The horizontal force would be going into the wheel in order to make it move and the wheel itself would be accelerating? Maybe?
You have translational acceleration and rotational acceleration.

How would you use each acceleration to determine where the total force goes?

the first part is fairly simple.

use the equation F=ma so what you do is do get 8.9*0.76=actual F
then do 15-Factual=frictional force.

however i can not help you with the secound part as i have never done it.

I have no idea how I would use the two accelerations to determine where the total force goes...

LowlyPion
Homework Helper
What is the formula for Torque?

Since the force is directed through the Center of Mass, you have a Torque about the axle given by the the moment of the force with the ground at the radius of the wheel.

So you are at once accelerating the wheel forward horizontally, as well as rotationally accelerating the wheel.

Torque = (r)(F)(sin(theta)), but what would I do with that equation?

You really need to start with a Free Body Diagram to see what forces act where. Then you can start writing the relevant force and moment equations and the kinematic relations.

dude i gave you the anser to part a) part b) however i now know what you must do you need to use the resistants calulated in part a and then put it into the torque equation

By 'rotational inertia' I am assuming it means the moment of inertia of the body.
Someone already told you the first part, that is basically using Newton II. Ignore the free body diagram initially for part one, think about translational movement only.

For part two, you need the answer to part 1. As someone said, draw a free body diagram, everytime. The correct formula for torque is rxF or as you stated rFsintheta. Think of where the friction from the surface will act on the body, and in which direction. You will see a part of rFsintheta becomes 1 which simplifies things. You can then use a fundamental thing for these problems, the condition for non-slip rolling.