Drum brakes were one of the first type of brake systems developed and are still in use today. The physics for drum brakes are the same as disk brakes. The law of conservation of energy basically states that energy cannot be created or destroyed only changed. What brakes do then is, through friction, convert the kinetic energy of the moving vehicle to heat. The heat must then be handled for the vehicle to stop properly.
How drum brakes work:
Drum brake systems are more complicated that a disk brake system and take more ongoing maintenance. The inherent design of a disk brake system makes it self-adjusting whereas a drum brake system needs to be mechanically adjusted.
When you step on the brake pedal, brake fluid pressure is directed from the brake master cylinder to the drum brake wheel cylinder. Inside the wheel cylinder are 2 rubber cups and 2 pistons. The fluid pressure pushes these 2 pistons apart expanding the brake shoes into an outer drum. Notice in the image there is a primary and a secondary shoe. The primary shoe has less friction material. This is because the action of the turning drum will try to twist the shoes, since the primary shoe is connected to the secondary shoe through the adjuster the primary shoe will force the secondary shoe tighter into the drum making the secondary shoe generate more friction. As a result drum brakes work better when going in a forward direction compared to backing up. All the heat that is generated has to be dissipated by the drum. As the friction material wears the brakes have to be adjusted to keep them working properly. This is accomplished by using a threaded star wheel adjuster very much like a bolt and nut, a lever and spring to make the adjustment and a cable to pull the lever. When the brakes are applied the shoes move out, the cable is pulled so the adjusting lever is lifted. When you stop braking the adjusting lever spring will pull the lever down keeping the cable tight. Once the shoes have worn enough the adjusting lever will catch on a knob of the star wheel so as the spring pulls the lever down the star wheel will turn threading the adjuster out. One of the biggest problems in a drum brake system is there is nowhere for the brake dust to go as the shoes wear. Eventually this dust will gum up the adjusting lever stopping it from turning. Then the brakes will wear out of adjustment and function poorly. This will be noticed as excessive brake pedal travel and poor park brake operation. The dust itself trapped in the drum will act like a lubricant further diminishing the brake operation. Should your vehicle have a common disk (front) drum (rear) brake system this puts excess strain on the front disk brakes which will case excessive wear, overheating, vibration issues and the car to dive while braking. With slippery road conditions it can even cause loss of control of the rear of the vehicle resulting in spins and skids leading to crashes. This is why it is so important to have drum brakes serviced and adjusted every so often.