Newton's Laws and Free Body Diagrams

Unit 2, Force and Translational Dynamics, is the heaviest unit of AP Physics 1 at 18 to 23 percent of the exam. Almost every force question is solved the same way: draw the forces, choose axes, then apply Newton's second law along each axis.

Newton's three laws

• First law: with zero net force, an object keeps its velocity. Constant velocity and rest are the same case.
• Second law: ΣF = ma, applied separately along each axis.
• Third law: forces come in pairs that act on different objects. A normal force and a weight on the same book are not a third law pair.

Drawing a free body diagram

1. Draw only the object you are studying, as a dot or a box.
2. Add one arrow for every force that acts on it: weight, normal force, tension, friction, applied forces.
3. Never draw ma as a force. It is the result of the forces, not one of them.
4. Choose axes along the acceleration. On a ramp, tilt the axes so one lies along the slope.

Normal force and friction

• The normal force is whatever the surface needs to push. It equals mg only when nothing else acts vertically and the vertical acceleration is zero.
• Static friction adjusts up to a maximum: f_s ≤ μ_s N.
• Kinetic friction is fixed once sliding starts: f_k = μ_k N.

Worked example

A 4 kg block is pulled across a floor by a 30 N rope at 37° above the horizontal. The coefficient of kinetic friction is 0.25. Take g = 10 m/s², sin 37° = 0.6 and cos 37° = 0.8. Find the acceleration.

1. Vertical axis, no acceleration: N + 30 × 0.6 − 40 = 0, so N = 22 N.
2. Friction: f = 0.25 × 22 = 5.5 N.
3. Horizontal axis: 30 × 0.8 − 5.5 = 4a, so 18.5 = 4a and a ≈ 4.6 m/s².

The common mistake is to write N = mg = 40 N. The rope pulls partly upward, so the floor pushes less and friction is smaller.

Connected objects

For objects linked by a rope or in contact, first treat them as one system to find the shared acceleration, then isolate one object to find the internal force. Internal forces cancel in the system equation.

The free response approach

• Draw the diagram first, with labeled arrows and no extra forces.
• Write the equation symbolically before putting numbers in. AP Physics 1 rewards the derivation, not only the final number.
• Justify in words when asked: name the forces and say which is larger and why.