Force, inertia and Newton's first law; inertial and non-inertial frames
A body keeps its state of rest or steady straight-line motion until a net external force acts. This resistance to change is inertia, measured by mass.
What a force can do
- A force is a push or a pull. It is a vector: it has a size and a direction.
- We cannot see a force. We see only its effects.
- A force can change the shape or size of a body, as when you squeeze a balloon.
- A force can start, stop, speed up, slow down or turn a moving body.
- A force can rotate a body about an axis, as when you open a door.
- When several forces act together, add them as vectors. Their single equivalent force is the net force (resultant).
How a net force changes motion
| Direction of the net force | Effect on the body | Everyday example |
|---|---|---|
| Along the motion | Speed increases | A mango falling from a tree goes faster and faster |
| Opposite to the motion | Speed decreases | A bicycle slows down when the brakes are pressed |
| At right angles to the motion | Only the direction changes; the speed stays the same | A stone whirled round on a string |
| Zero (forces balance) | Velocity does not change; a body at rest stays at rest | A book lying on a table |
From Galileo to the first law
Galileo noticed that a ball speeds up rolling down a slope and slows down rolling up one. On a level, smooth surface it should do neither, so it should keep moving. He also let a ball roll down one slope and up a facing slope. It rose to nearly the same height. As the second slope was made less steep, the ball went farther. If that slope became level, the ball would roll on for ever, with no friction. Newton turned this into his first law of motion. It is also called the law of inertia. Why must we keep pushing a trolley at steady speed? Our push only balances friction, so the net force is zero.
Inertia in daily life
- Inertia of rest: when a bus starts suddenly, standing passengers fall backward. Their feet move with the bus, but the upper body tends to stay at rest.
- Inertia of motion: when a moving bus stops suddenly, passengers fall forward. Their bodies tend to keep moving.
- Inertia of direction: when a bus takes a sharp turn, passengers lean outward. Their bodies tend to keep moving in a straight line.
- Beat a hanging carpet with a stick: the carpet moves, but the dust stays at rest and falls off.
- Put a coin on a card over a glass. Flick the card away quickly: the coin stays behind and drops into the glass.
Inertial and non-inertial frames of reference
A box lies on a railway platform. A person on the platform sees it at rest. A passenger in a train moving at steady velocity v sees it moving at −v, still with no acceleration. A passenger in a train speeding up at a sees it accelerate at −a, although no force acts on it.
Worked example: pseudo force in a bus
A 60 kg passenger stands in a bus that speeds up at 2 m s⁻². What pseudo force seems to act on the passenger in the bus frame? What force keeps the passenger at rest relative to the bus?
- The bus is accelerating, so it is a non-inertial frame.
- Pseudo force = ma = 60 kg × 2 m s⁻² = 120 N.
- It acts opposite to the bus's acceleration, that is, towards the back of the bus.
- To stay at rest in the bus, a real force of 120 N must act forward. This is the friction of the floor on the feet (helped by a hand on the rail).
Pseudo force 120 N towards the back of the bus; it is balanced by 120 N of friction from the floor acting forward
Seat belts and airbags in cars and buses work against inertia. In a sudden stop your body keeps moving forward, and the belt supplies the force that stops you safely.
1 marks: “Which physical quantity is a measure of the inertia of a body?” Its mass. A larger mass means a larger inertia.
2 marks: “State Newton's first law of motion. Why does a standing passenger lurch forward when a moving bus brakes hard?” Law: a body remains at rest or in uniform motion in a straight line unless a net external force acts on it. When the bus slows, the feet slow with it, but the upper body keeps moving forward because of its inertia of motion.
2 marks: “What is an inertial frame of reference? Is a car going round a sharp bend at constant speed an inertial frame? Give a reason.” An inertial frame is at rest or moves with constant velocity, and the law of inertia holds in it. No: the car's direction of motion changes, so it is accelerating and is a non-inertial frame.
First law = law of inertia: no net force, no change in velocity.