Newton’s first law of motion

What is Newton’s first law?

In an inertial frame, every body continues in its state of rest, or of uniform motion in a straight line, unless a net external force acts on it.

A body at rest stays at rest, and a moving body keeps moving with the same speed in the same direction. In both cases its velocity does not change unless a net external force acts on it.

Notice the word net. A body can have several forces on it and still obey the first law, as long as they add up to zero. A book on a table is pulled down by its weight and pushed up by the table, and the two balance.

Inertia and mass

Every body resists a change in its state of rest or of uniform motion. This property is called inertia, so the first law is also called the law of inertia.

Inertia shows up in three ways:

• Inertia of rest. When a bus starts suddenly, standing passengers fall backward: their feet move with the bus while the upper body tends to stay at rest.
• Inertia of motion. When the bus brakes suddenly, the passengers lurch forward: their feet stop with the bus while the upper body keeps moving.
• Inertia of direction. When a car takes a sharp turn, the passengers feel pushed outward, because their bodies tend to continue in a straight line.

Mass is the measure of inertia for translational motion (motion of the body as a whole, without rotation). The larger the mass, the harder it is to start, stop or change the direction of a body’s motion. A loaded truck is much harder to set moving than a bicycle because it has far more mass.

The first law as an equation

Here $\vec F_{\text{net}}$ is the vector sum of all the external forces on the body and $\vec v$ is its velocity. A constant velocity means zero acceleration, $\vec a = 0$, and a particle with zero net force is said to be in equilibrium (an extended body also needs zero net torque, so that its rotation does not change). When the net force is not zero, Newton’s second law of motion tells you how fast the velocity changes. Because force is a vector, the condition holds along each axis separately:

Examples from everyday life

• Tightening a hammer head. Strike the bottom of the handle on the floor: the handle stops, but the loose head keeps moving down and wedges tighter onto it.
• Dusting a carpet. Beat a hanging carpet with a stick: the carpet moves suddenly, but the dust tends to stay at rest, so it separates and falls off.
• A coin on a card over a glass. Flick the card away sharply and the coin, at rest, stays behind and drops into the glass. The card’s friction acts on it for too short a time to move it much.

Inertial frames of reference

The first law does not hold for every observer. In a bus that is speeding up, a ball on a smooth (frictionless) floor slides backward relative to the bus, although no horizontal force acts on it: seen from the bus, it accelerates with zero net force.

A frame of reference in which the first law holds is called an inertial frame. So the first law also defines the frames in which Newton’s laws can be used. Any frame translating at constant velocity relative to an inertial frame, with non-rotating axes, is also inertial, and in most Class 11, JEE and NEET problems the ground is taken as one (to a good approximation: the Earth’s rotation makes it slightly non-inertial).

Common mistakes to avoid

Quick revision summary

• A body stays at rest, or in uniform motion in a straight line, unless a net external force acts on it.
• Zero net force means zero acceleration: the velocity stays constant, and a particle is in equilibrium.
• Inertia is the tendency of a body to resist a change in its state of motion; mass is its measure.
• The law holds only in inertial frames, and it defines them.

Questions students ask

What is the difference between inertial and non-inertial frames?

An inertial frame is one in which Newton’s first law holds, while a non-inertial frame accelerates relative to an inertial one, so the first law fails in it. Seen from a turning merry-go-round or a braking car, a body with no net force on it seems to accelerate. Newton’s laws can still be used in a frame that moves with acceleration a₀ without rotating, by adding a pseudo force −ma₀ to every body; an inertial frame needs no pseudo force.

How does Newton’s first law define force?

Newton’s first law gives a qualitative definition of force: a force is whatever changes, or tends to change, a body’s state of rest or of uniform motion in a straight line. The second law then makes it quantitative, F = dp/dt, which for constant mass is F = ma.

What is the difference between Newton’s first and second laws?

Newton’s first law describes a body with zero net force, whose velocity stays constant, while the second law, F_net = dp/dt, gives how fast the momentum changes when the net force is not zero. Putting F_net = 0 in the second law gives the first, but the first law is still stated on its own, because it defines the inertial frames in which the second law holds.

Is the Earth an inertial frame of reference?

The Earth is very nearly, but not exactly, an inertial frame. Its spin gives a point on the equator a centripetal acceleration of about 0.034 m s^⁻², and its orbit gives an acceleration of about 0.006 m s^⁻² towards the Sun, both far smaller than g = 9.8 m s^⁻². So for most problems the ground is treated as an inertial frame.

Practice questions

Try each question first, then open the answer to check your working.

1. Q1. A car moves along a straight, level road at a constant 20 m s⁻¹. What is the net force on the car?

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   Zero. The velocity is constant, so $\vec a = 0$ and $\vec F_{\text{net}} = 0$. The forward friction from the road on the driving wheels balances air resistance and rolling friction.

2. Q2. A ball of mass 0.5 kg hangs at rest from a string. Find the tension in the string. Take g = 9.8 m s⁻².

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   The ball is at rest, so the net force is zero: T − mg = 0. So T = mg = 0.5 × 9.8 = 4.9 N.

3. Q3. An astronaut accidentally gets separated from a small spaceship that is accelerating at 100 m s⁻² in interstellar space, far from any star (NCERT Example 4.1). What is the astronaut’s acceleration just after leaving the spaceship?

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   Approximately zero relative to an inertial frame, neglecting distant gravitational forces and the small spacecraft’s gravity. Relative to the spacecraft, the astronaut’s acceleration is 100 m s^⁻² opposite to the spacecraft’s acceleration. By the first law the astronaut moves on with the velocity the spaceship had at the instant of separation; only the spaceship keeps accelerating.