# Wheel Rotation: Force, Mass, Radius, Acceleration

• Cherrybawls
In summary: However, you could also choose a different axis, like the point where the wheel touches the ground, in which case, the applied force would also create a torque.In summary, the problem involves a wheel with a horizontal force applied to its center of mass and a tangential frictional force at its point of contact with the ground. To solve the problem, you must consider both torques and forces, and the choice of axis will determine which forces create a non-zero torque. The rotational inertia of the wheel about its center of mass can be found by using the equation τ=Iα.
Cherrybawls

## Homework Statement

A constant horizontal force Fapp of magnitude 10N is applied to a wheel of mass 10kg and radius .3m. The wheel rolls smoothly on the horizontal surface, and the acceleration of its center of mass has magnitude .6 m/s2 (a) In unit-vector notation, what is the frictional force on the wheel? (b) what is the rotational inertia of the wheel about the rotation axis through its center of mass?

## Homework Equations

I don't even know

## The Attempt at a Solution

I spent more than an hour on this and I could not figure it out. Needless to say I am extremely frustrated because it seems as though my teacher has not taught us anything we need to know to solve this, so I don't think any of my work is worth typing in this space.

Start with a free-body diagram. Identify all the forces on the wheel and where they act.

The applied force is horizontal on the center of mass and then there is a tangential frictional force going in the opposite direction on the bottom of the wheel where it is in contact with the ground. And of course there is the normal force. Does the frictional force create torque or does the applied force, it seems to me that it would be the frictional force. And is this problem solved using torque? I am really at a loss for where to even begin

You forgot to mention the wheel's weight. That's the only other force.

In problems that combine rotational and translational motion, you need to consider both torques and forces. In other words, you want to apply both F=ma and τ=Iα.

As to the question of which forces exert a torque, that depends on where you choose to set your axis. A natural choice would be the center of mass of the wheel, in which case, you'd be right that only the frictional force results in a non-zero torque.

## 1. How does force affect wheel rotation?

The amount of force applied to a wheel affects its rotation by causing it to accelerate or decelerate. This is described by Newton's Second Law of Motion, which states that the force applied to an object is equal to its mass multiplied by its acceleration.

## 2. Why does mass impact wheel rotation?

The mass of a wheel affects its rotation because it determines how much inertia the wheel has. Inertia is the resistance of an object to changes in its motion, so a heavier wheel will be harder to accelerate or decelerate than a lighter wheel.

## 3. How does the radius of a wheel affect its rotation?

The radius of a wheel has a direct impact on its rotation because it determines the distance from the center of the wheel to the point where force is applied. A larger radius will result in a greater torque, or rotational force, being applied to the wheel.

## 4. What is the relationship between acceleration and wheel rotation?

Acceleration and wheel rotation are directly related. The greater the acceleration, the faster the wheel will rotate. This is because acceleration is the rate of change of velocity, and rotation is a type of velocity.

## 5. How does friction affect wheel rotation?

Friction can have both a positive and negative impact on wheel rotation. On one hand, friction between the wheel and the surface it is rolling on can slow down the rotation of the wheel. On the other hand, friction between the wheel and an axle or bearing can help maintain the rotation of the wheel by preventing it from sliding or slipping.

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