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A pulley that moves twice as far as the load it lifts. A crate that slips on a truck that starts too hard. A toy that swings forward in a braking bus. Here Newton's laws meet many bodies at once: strings and constraints, stacked blocks and wedges, accelerating and rotating frames, and loops and banked bends. The problems are at the level of JEE Advanced, A-Level Physics and IB Higher Level, with a long timed paper.

What's inside

1. Strings, pulleys and constraint relations: A string that cannot stretch links the motions of the bodies it joins. Write the length of the string as a constant and differentiate it twice. The result is a constraint relation. It gives the extra equation that movable pulleys and slanting strings need.
2. Stacked blocks, wedges and friction on several surfaces: When one body rides on another, friction decides whether they move together. Guess that they do, find the friction that this needs, and compare it with the largest friction that the surfaces can give. A wedge that is free to move adds one more body and one more equation.
3. Pseudo forces and circular dynamics: Newton's laws hold in a frame that does not accelerate. In a frame that does, we add a pseudo force to every body and the laws work again. With this idea, and with the rule that the net force toward the centre is $mv^2/r$, we solve banked roads, conical pendulums and vertical circles.