Category: wheels

Why is it that we can use energy without doing work? Where does this energy go? For example, you could push on a wall until your arms fell off, but you wouldn’t have done any work.

When you are pushing on something without doing any work, your energy is being converted directly into thermal energy inside your body. Your muscles are inefficient and they convert food energy into thermal energy whenever they are under tension. It’s like a car, which uses gasoline even when it’s stopped at the light. The engine keeps running but it does no work. Similarly, if you simply burned your cereal in your breakfast bowl, you would turn its energy directly into thermal energy without doing any useful work. Your body is also able to burn up that food energy and create thermal energy, albeit a little less visibly.

Why is the frictional force on a wagon’s wheel in the opposite direction from the frictional force on a car’s wheel?

When you pull a wagon forward, friction from the ground starts the wheel turning and it does this by pushing backward on the bottom of the wheel. Friction is thus preventing the wheel from skidding across the pavement. When you step on a car’s accelerator, the car’s engine starts the wheel turning and friction from the ground pushes forward on the bottom of the wheel to prevent the wheel from skidding across the pavement. In the first case, friction is trying to help the wheel to turn while in the second case friction is trying to keep the wheel from turning. That’s why the forces (and the resulting torques) on the wheel are in opposite directions for the two cases.

I didn’t understand how a car (or wagon) starts its motion.

A wagon starts its motion when you pull it or push it. If its wheels weren’t touching the ground, they would simply move along with the wagon and would not turn. However, they are touching the ground and the ground exerts a backward frictional force on them to keep them from sliding on the ground. This backward frictional force causes the wheels to begin turning.

A car starts its motion when the engine of the car exerts a torque on its wheels. These wheels begin to rotate. However, the wheels are again touching the ground and the ground exerts a frictional force on the wheels to keep them from skidding. This frictional force not only opposes the wheels’ angular acceleration, it also causes the wheels and the car to which those wheels are attached to accelerate horizontally.

In the book, you discussed pushing on a file cabinet that was resting on the sidewalk. Why doesn’t the file cabinet move when you push even a little — you’re making the net force greater than zero?

When you exert a small horizontal force on the file cabinet, it doesn’t move because static friction between the ground and the file cabinet exerts a second horizontal force on the file cabinet that exactly balances your force. If you push the file cabinet west, the ground will exert a static frictional force on the file cabinet, pushing it east. The file cabinet will thus experience a net force of zero. You’ll have to push very, very hard before static friction will be unable to match your force. One you do exceed the limit of static friction, the friction will no longer be able to balance your force and the file cabinet will experience a net force in the horizontal direction. The file cabinet will then accelerate in the direction of your force.

Is a spinning toy top a perfect example of angular momentum?

Yes. If you spinning it about a vertical axis (so that gravity doesn’t exert a torque on it about its point), it will spin at a steady angular velocity almost indefinitely. Sliding friction does slow it gradually but if the point is very sharp, sliding friction there exerts very little torque on the top about its rotational axis. Because it’s unable to exert a torque on the ground, the top can’t exchange angular momentum with the earth. It spins on until it slowly gets rid of its angular momentum through sliding friction and air resistance.

What exactly is the different between momentum and inertia?

Inertia is a concept—the property of an object to resist any change in its velocity. Momentum is a vector quantity—the product of an object’s mass times its velocity and an important characteristic of a moving object. Momentum is important because it’s conserved and it’s conserved in large part because of inertia and related concepts.