What is Linear Momentum? Formula and Direction

Physics · Laws Of Motion · NEET

Linear momentum is the "amount of motion" in a moving body. It equals mass times velocity: p = mv. It is a vector, so it always points in the same direction as the velocity. Memory hook: a slow heavy truck and a fast light bike can carry the SAME momentum, because momentum cares about BOTH mass and speed, not just speed.
Momentum is a vector: p = m v (points along velocity)Small mass, high speed2kgv = 10 m/sp = 2 x 10 = 20 kg m/sLarge mass, low speed20kgv = 1 m/sp = 20 x 1 = 20 kg m/sSame momentum (20 kg m/s) from different mass x speed
Two very different bodies can carry equal linear momentum: a light fast block (2 kg at 10 m/s) and a heavy slow block (20 kg at 1 m/s) both give p = 20 kg m/s. The arrow (velocity) also shows momentum's direction, since p = mv is a vector.

Your doubts, answered

Is linear momentum a vector or a scalar?

Momentum is a vector. Since p = mv and mass m is a positive scalar, p points in the exact same direction as the velocity v. This is why NEET asks about the DIRECTION of momentum, not just its size. A ball moving east has eastward momentum; the same ball moving west has westward momentum (opposite sign).

What is the difference between momentum and velocity?

Velocity tells you how fast and in which direction a body moves. Momentum also includes the mass: p = mv. Two bodies can have the same velocity but different momentum if their masses differ. A loaded truck and a small car moving at the same speed have very different momentum because the truck has much more mass.

What is the SI unit of linear momentum?

The SI unit is kilogram metre per second, written kg m/s. You get it by multiplying mass (kg) by velocity (m/s). There is no special name for this unit. It can also be written as newton-second (N s), because 1 N s = 1 kg m/s.

Can two objects with different masses have the same momentum?

Yes. Momentum is mass times velocity, so a small mass with a high velocity can match a large mass with a low velocity. Example: a 2 kg body at 10 m/s has p = 20 kg m/s, and a 20 kg body at 1 m/s also has p = 20 kg m/s. This is a common NEET idea used in collision and recoil problems.

If speed stays the same but direction changes, does momentum change?

Yes. Momentum is a vector, so a change in direction is a change in momentum even if the speed (magnitude) is constant. A body moving in a circle at constant speed has constant momentum magnitude but its momentum direction keeps changing, which is why a force (centripetal) is needed. This is a favourite NEET trap.

⚠️ The NEET trap
The speed did not change, so the momentum did not change and no force acts.
Momentum is a vector. If direction changes, momentum changes even at constant speed, so a force must act. In the NEET 2023 football-player question, the player keeps the same speed but turns from south to east, so his momentum changes direction and the force points North-East.
🧠 Constant speed does NOT mean constant momentum.

Real NEET questions

NEET 2023

A football player moving southward suddenly turns eastward with the same speed to avoid an opponent. The force that acts on the player while turning is directed:

A · Eastward
B · Northward
C · North-East
D · South-West
Solution: Force acts in the direction of the change in momentum, F is along Δp = p_final − p_initial. Take momentum size as p (mass × speed) since speed is the same before and after. Initial momentum (southward) = −p ĵ. Final momentum (eastward) = +p î. So Δp = p î − (−p ĵ) = p î + p ĵ. This vector has equal east and north parts, so it points North-East. Answer: C. Key idea: even though the SPEED did not change, the DIRECTION of momentum changed, so there is a change in momentum and a force must act.

Solved Laws Of Motion NEET PYQs

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Frequently asked

What is linear momentum in simple words?

Linear momentum is how much motion a body has. It is found by multiplying mass by velocity, p = mv. A heavier or faster body has more momentum, and it is harder to stop.

What is the formula for linear momentum?

The formula is p = mv, where m is mass in kg and v is velocity in m/s. Because velocity is a vector, momentum is also a vector pointing the same way as the velocity.

What is the SI unit and dimensional formula of momentum?

The SI unit is kg m/s (also written N s). The dimensional formula is [M L T^-1].

Why is momentum important for NEET Laws of Motion?

Newton's second law is really about the rate of change of momentum, and conservation of momentum solves collisions, recoil, and explosion problems. Getting momentum's vector direction right is needed for many NEET questions and connects directly to the next topic, Newton's second law.

Is momentum the same as inertia?

No. Inertia is a body's resistance to change in its motion and depends only on mass. Momentum depends on both mass and velocity, and it is a vector. A body at rest has inertia but zero momentum.