Where does energy go when you try to push a heavy object and it doesn’t move? Thermal energy isn’t made, so why do people get tired?

While it’s true that there is no thermal energy made by static friction, since the object doesn’t slide, your body can still make thermal energy directly. You get tired because your muscles must turn useful food energy into thermal energy whenever they are under tension. If you are doing work, they also convert food energy into that work, but even when they aren’t doing work, they still convert food energy into thermal energy.

What’s going on with the wheels when a car accelerates?

As a car heads forward, its freely turning wheels begin to rotate. The torque that starts them rotating comes from static friction with the ground. The ground pushes backward on the bottoms of the wheels to keep them from sliding and this backward frictional force exerts a torque on the wheels. They begin to rotate so that their bottom surfaces head backward and their top surfaces head forward.

The car’s powered wheels turn for a different reason: they are driven by a torque from the car’s engine. As you step on the accelerator, the engine exerts a torque on the wheels and they begin to turn. They would skid backward across the ground where it not for static friction between the wheels and the ground. This static friction opposes the skidding by exerting a forward force on the bottom surface of the wheels. This static frictional force produces a torque on the wheels and that torque partly balances the torque from the engine. The wheels don’t skid and they’re angular velocities increase relatively slowly. However, the forward frictional force on the wheel’s bottom surface isn’t balanced elsewhere in the car and the car experiences a forward net force. The car accelerates forward.

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.

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.

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.

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.