Motion & forces

The big picture

A moving object does not carry a force in the direction of its motion. Forces describe interactions; velocity describes how position changes. Keeping those ideas separate is the first big step towards solving mechanics reliably.

Work through a motion graph, draw the body you are analysing, and then connect the graph to a force equation. A clear choice of system and axes usually saves more work than memorising another special-case formula.

What to read, and why

Start at the first stage if the subject is new. Otherwise, use the descriptions to find the missing step in your understanding. All chapter explanations are open; the labels identify chapters whose solutions and answer checks are also free.

1. STAGE 1

   Describe the change

   Learn what the slope and area mean, then decide whether constant acceleration is justified.

   Velocity and acceleration →Read motion as changing position—and changing velocity4 worked examples · 6 checks · Complete free chapterMotion with constant acceleration →Derive the equations, choose an interval, and know when a calculated answer stops describing the motion.4 worked examples · 7 checks · Open explanation · member practiceProjectile motion and moving observers →Use one clock for both axes, then simplify encounters by comparing relative positions and velocities.8 worked examples · 8 checks · Open explanation · member practice

2. STAGE 2

   Explain the change

   Draw only forces on the chosen body; test whether static friction can supply the required value.

   From interactions to equations →Learn to choose a body, draw its forces, and explain a change of motion before calculating it.4 worked examples · 7 checks · Open explanation · member practiceStatic friction: find what is needed →Replace “friction equals μN” with a method that tests whether surfaces can remain at rest relative to each other.4 worked examples · 8 checks · Open explanation · member practice

3. STAGE 3

   Connect constraints

   Translate string length or circular geometry into conditions before solving the forces.

   Connected bodies, sliding friction and accelerating frames →Build force equations from the system, the contact state and the geometry of each connection.9 worked examples · 8 checks · Open explanation · member practiceForces that turn a moving object →Derive inward acceleration, resolve real forces and test the limits of circular motion.6 worked examples · 6 checks · Open explanation · member practice

Choose a method before an equation

Use the physical conditions to narrow the choices. A formula becomes useful after you know why its model applies.

Try a complete free problem

These problems include the hints, worked reasoning and answer feedback. Attempt one before opening the solution.