Unit Of Momentum - SI Unit, Other Units And FAQ - Vedantu

Momentum is a fundamental concept in Physics and is essential for understanding motion, collisions, and the effects of forces on objects. Momentum describes the quantity of motion that an object possesses due to its mass and how fast it is moving. It helps explain everyday phenomena such as why heavier vehicles are harder to stop or how sport balls carry force as they move.

Definition and Formula of Momentum

In Physics, momentum is defined as the product of an object's mass and its velocity. The formula for momentum is:

p = m × v

Here, p represents momentum, m is the mass of the object, and v is its velocity. Both mass and velocity are key factors — if either increases, so does the momentum.

SI Unit of Momentum: Stepwise Derivation

The SI (International System of Units) unit of momentum is derived from its formula p = m × v. The SI unit for mass is kilogram (kg), and the SI unit for velocity is meter per second (m/s). Multiplying these gives the SI unit of momentum:

Momentum SI Unit = kilogram × meter/second = kg·m/s

Therefore, the SI unit of momentum is kg·m/s.

Key Example: Calculating Momentum

Suppose a moving object has a mass of 2 kg and a velocity of 3 m/s.

Momentum (p) = 2 kg × 3 m/s = 6 kg·m/s

So the object's momentum is 6 kg·m/s. This unit expresses the amount of motion contained in the object.

Relationship Between Force and Momentum

When a force acts on an object for a period of time, it changes the object's momentum. This concept links to impulse in Physics, which equals the change in momentum over a time interval. Impulse (J) = Force (F) × time (t).

Impulse = F × t = Δp

The unit for impulse is Newton-second (N·s), which is dimensionally equal to kg·m/s. Hence, both kg·m/s and N·s can represent momentum in SI.

Units of Momentum: Table Comparison

System	Unit	Symbol	Equivalent in SI
SI	kilogram meter per second	kg·m/s	kg·m/s
Alternate (SI)	Newton second	N·s	1 N·s = 1 kg·m/s
CGS	gram centimeter per second	g·cm/s	1 kg·m/s = 100,000 g·cm/s

Step-by-Step: Solving a Momentum Problem

1. Identify the mass (m) and velocity (v) of the object.
2. Write the formula: p = m × v.
3. Substitute the known values.
4. Multiply and include the correct SI unit (kg·m/s).

Another Example

A ball with mass 0.2 kg moves with a velocity of 5 m/s. Calculate its momentum.

Momentum = 0.2 kg × 5 m/s = 1 kg·m/s

Therefore, the momentum of the ball is 1 kg·m/s.

Key Points and Physical Meaning

• Momentum combines both mass and velocity, making it a vector quantity pointing in the direction of motion.
• If velocity is zero, then momentum is also zero, regardless of the mass.
• Greater mass or velocity means greater momentum.
• The SI unit kg·m/s is always used for momentum in calculations and Physics questions.

Key Formulas for Application

Concept	Formula	SI Unit
Momentum	p = m × v	kg·m/s
Impulse	J = F × t = Δp	N·s or kg·m/s
Force (From Momentum)	F = Δp / t	N (Newton)

Practice and Explore Further

• Test your understanding of unit of momentum problems.
• Study the impulse-momentum theorem for collisions and force calculations.
• Understand how mass and momentum are related.
• See detailed applications in conservation of linear momentum in closed systems.

Summary

Momentum is the product of mass and velocity, and its SI unit is kg·m/s. This concept is crucial for solving problems related to motion and collisions. A clear understanding of units, formulas, and practical calculations will aid in mastering Physics fundamentals and scoring well in competitive exams.