Force and Gravitation
Force and Gravitation covers Newton's laws, inertia, momentum, action-reaction pairs, the universal law of gravitation, and the difference between mass and weight. Numerical work commonly uses F = ma and W = mg.
Core ideas
- First law: a body keeps its state of rest or uniform motion unless a net external force acts. This is inertia.
- Second law: net force F = ma; momentum p = mv; force is the rate of change of momentum.
- Third law: every action has an equal and opposite reaction on a different body.
- Universal gravitation: F = G m1 m2 / r^2, where G = 6.67 x 10^-11 N m^2 kg^-2.
- Acceleration due to gravity g = GM/R^2, about 9.8 m/s^2 near Earth's surface. Weight W = mg is a force; mass is the amount of matter.
- g is less at the equator than at the poles and decreases with height; it is about one-sixth on the Moon.
Worked example
A 10 kg body is taken from Earth to the Moon. Find its mass and weight on the Moon, taking g on Earth as 9.8 m/s^2 and lunar g as one-sixth of Earth's. Mass stays 10 kg. Earth weight = 10 x 9.8 = 98 N. Moon weight = 98/6 = 16.3 N. Reasoning: mass is constant, but weight depends on the local gravitational field.
Traps that cost marks
Action and reaction forces do not cancel because they act on different bodies. Do not say a rocket moves because it pushes on the ground; it moves by expelling gas backward. Weight is in newtons, not kilograms. In F = ma, use the net force, not any single force.