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Unit of momentum is the product of the units between mass and velocity. As per SI unit of momentum, if the mass is expressed in kg and velocity is expressed in meters per second, then in that case the momentum will be expressed in kilogram meters per second (kg.m/s).
Momentum can be described as the product of mass and velocity. Momentum is a vector quantity with both magnitude and direction. Mathematically, it can be represented as: p = mv
As per Newtonian mechanics, translational momentum, linear momentum, or simply momentum can be expressed as the product of the mass and velocity of an object. A body’s momentum depends on its mass and velocity of it. Assuming that either of the two values is zero, the momentum tends to become zero.
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Key Terms: Momentum, Motion, Vector, Velocity, Mass, Newton’s Laws of Motion, Force, Magnitude, Linear Momentum
What is Momentum?
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Momentum is the product of mass of a particle and its velocity.
- Momentum is having both direction and magnitude. Hence, it is considered a vector quantity.
- According to the second law of motion of Newton, it states that – “the rate of change of momentum is equal to the force acting on the part”.
Momentum of Collision
- From this law, we get that if some constant force is acting on a particle for a given period of time, the force of the product and the time of the product will be equal to the change in momentum.
- Also, we can say that the momentum of a particle is the measure of time required for some constant force to bring the particle to rest.
- The Momentum becomes zero, if either of the values of mass or velocity is zero. Mathematically the formula is:
| P = m \(\times\) v |
Here,
- p represents momentum
- m represents mass
- v represents velocity
Dimensional Analysis Video Explanation
What is Impulse?
Impulse ( represented by J or Imp), in Classical Mechanics, is the integral of a force, F, over the time interval, t.
- Now, because force is a vector volume, the impulse is considered a vector volume.
- Impulse, that has been applied to an object, is seen to yield an original vector change in its direct impulse, also in the attendant direction.
- The SI unit of impulse is the Newton second (Ns), and the dimensionally original unit of impulse is the kilogram cadence per second (kg ⋅ m/ s).
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Unit of Momentum
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There is no particular name for the unit of Momentum as it is a product of velocity & mass whose units are expressed in quantities. So, the mass is measured in kg and velocity is measured in ms-1. So the derived SI Unit for momentum is kg ms-1.
Derivation of Unit of Momentum
The momentum of a certain object is represented by the symbol ‘p’.
The mathematical equation of momentum of the object is, p = m \(\times\) v
Where,
- m = mass of a particle
- V = velocity of the particle
The equation above describes the fact that the mass and velocity of the particle is directly proportional to the momentum of that particle.
Hence, the SI unit that we get of the momentum of a body/ particle is the product of its mass (Kg) and its velocity (ms-1). Hence the SI unit of momentum can be written as kg ms-1.
For two particles, the momenta can be added in the following manner:
P = p1 + p2
= m1 v1 + m2 v2
In case of more than two particles, the momentum, will be added in following way: p = imi vi
A Particle Travels in a Circular Path
What does the momentum of a body depend upon?The momentum of a body generally depends upon both mass and velocity. Assuming that either of the two values becomes zero, then the momentum also becomes zero. What is Linear Momentum?Linear momentum is also considered under the hierarchy of momentum.
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Other Units of Momentum
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Considering a situation in which the force is equal to the rate of change of momentum:
Force = \(\frac{Change \ in \ Momentum}{Time \ Interval}\)
Thus, Change in momentum = Force \(\times\) time interval
Hence, the unit for momentum here can be written as Newton-second (Ns).
According to the CGS system, if we calculate the velocitobject/s and mass in grams, then the SI unit of momentum can be written as gram-centimetres per second i.e. (g.cm/s)
There are even few more units of momentum like kg\(\times\)mi/hr, kg\(\times\)km/hr and g\(\times\)cm/s. In every case, the unit of the mass of the object is multiplied by the units of velocity.
Momentum Units
The units of momentum are as listed below:
| Parameters | Values |
|---|---|
| SI Units | Kilogram Meter per Second (kg.m/s) |
| Common Symbols | p, p |
| Other Units | slug.ft/s |
| Dimension | MLT-1 |
Previous Year Questions
- The dimension of angular momentum is … [WBJEE 2012]
- A circular disc is rotating about its own axis … [CBSE Class XII]
- A shell of mass 10 kg … [WBJEE 2008]
- The position of both an electron and helium atom … [NEET 1998]
- If a ball of mass 0.1 kg hits …
- The orbital angular momentum of a p-electron is given as …
- A body of mass M kg initially at … [AMUEEE 1999]
- Identify the wrong statement … [AMUEEE 2009]
- System shown in figure is in equilibrium and at rest … [JEE Advanced 2006]
- The orbital angular momentum of an electron in 2s-orbital … [JEE Advanced 1996]
- The principle of conservation of linear momentum …
- A rocket is about to launch upwards from its platform … [TS EAMCET 2018]
Things to Remember
- The momentum itself does not have any SI unit. Hence, the product of the SI units of mass & velocity is used for the SI unit of momentum which is kg ms-1.
- The mathematical formula used to describe momentum is p = m x v.
- The direction of the velocity vector is the same as the direction of the momentum vector.
- If we consider the launch of a rocket, the initial momentum is zero. During the launch due to the exhaustion of expanding gases the downward momentum gets equalized with upward momentum. Hence, the total momentum remains constant i.e. zero.
- Momentum is a vector quantity which involves both the direction and the magnitude.
- Considering Newton’s Third law, all particles exerts equal and opposite forces on each other. So, the change in momentum in one particle will be balanced by some other particle with an opposite and equal change in momentum.
- The law of conservation of momentum is applied to all the interactions including the separation and collisions that are caused by explosive forces.
Unit of Momentum PDF
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Sample Questions based on Unit of Momentum
Ques. Is Momentum considered a Vector Quantity? (1 mark)
Ans. Momentum is considered a Vector Quantity. Momentum has both direction & Magnitude. As a vector quantity, an object must be described by both its direction as well as its magnitude.
Ques. An object with a changing speed will have a changing momentum. (True/False) (1 mark)
Ans. True
An object changing speed will have both changing velocity and momentum.
Ques. Momentum is a conserved quantity; the momentum of an object is never changed. (True/False) (1 mark)
Ans. False.
The momentum of an object is seen to directly vary with the speed of the object. As two objects of different mass move at the same speed; the object which is more massive will have the greatest momentum.
Ques. If a cart of 2.0kg is having a velocity of 8.0 m/s. What will be its momentum? (2 marks)
Ans. Here, the given mass (m) of the cart is 2.0kg. The velocity (v) of the cart is 8.0 m/s.
According to the formula:
p = m*v
p = 2.0 kg * 8.0 m/s
p =10.0 kgm/s
So, the momentum (p) of the cart is 10.0 kgm/s.
Ques. Define the conservation of Momentum principle. (2 marks)
Ans. The Principle of Conservation of Momentum states that, in an isolated system the total momentum of two objects will remain the same before and after the collision. The momentum here gets transferred between the objects during the collision due to which it is not destroyed in the process. For example, if we kick a football, the momentum is transferred from our foot to the football. Hence, football remains intact.
Ques. What are the types of collisions that Momentum depends on? (2 marks)
Ans. Momentum depends on the types of Collisions:
- Inelastic collision (Perfectly inelastic collision & Partially Inelastic collision) – This is the collision in which some K.E of the colliding bodies gets transformed into other forms of energy, either as heat or as sound. Example: traffic collision
- Elastic collision – in which no K.E.N gets transformed into heat or any other form of Energy. Ex – Collision between two balls in a pool game.
Ques. What is the impulse-momentum theorem? (2 marks)
Ans. Impulse is expressed by the symbol J and the SI unit is Newton-seconds (NS)
For some constant force, J = F. Δt
As we can see above, this is equal to a change in the momentum Δp. Hence, this theorem is called the impulse-momentum theorem.
Ques. Determine the momentum of the following: (3 marks)
(a) 60-kg halfback moving eastward at 9 m/s.
(b) 1000-kg car moving northward at 20 m/s.
(c) 40-kg freshman moving southward at 2 m/s.
Ans. b. The following answers can be seen:
- p = m \(\times\)v = 60 kg \(\times\) 9 m/s
p = 540 kg \(\times\) m/s, east - p = m \(\times\) v = 1000 kg \(\times\) 20 m/s
p = 20 000 kg \(\times\)m/s, north - p = m\(\times\)v = 40 kg \(\times\) 2 m/s
p = 80 kg \(\times\) m/s, south
Ques. A car possesses 20 000 units of momentum. What would be the car's new momentum if: (3 marks)
(a) its velocity was doubled.
(b) its velocity was tripled.
(c) its mass was doubled (by adding more passengers and a greater load)
(d) both its velocity was doubled and its mass was doubled.
Ans. a. p = 40 000 units (doubling the velocity will double the momentum)
- p = 60 000 units (tripling the velocity will triple the momentum)
- p = 40 000 units (doubling the mass will double the momentum)
- p = 80 000 units (doubling the velocity will double the momentum and doubling the mass will also double the momentum; the combined result is that the momentum is doubled twice-quadrupled)
Ques. An object which is moving at a constant speed has momentum. (True/False) (3 marks)
Ans. True.
One must also remember that to have momentum one might not be at a constant speed. In the case an object is seen to travel eastward and, gradually slowing down; then its momentum is considered to be westward. Momentum, in reality, is a conserved quantity; meaning that the momentum of an object does not change. Thus,
- Momentum can be defined as the product of mass & velocity.
- If the mass of an object is constant, thus the momentum of it will depend only on the speed of the object
Ques. The linear momentum of a ball is seen to be about 30 kg ms-1 with its mass almost only 5 kg. Thus, with the given values, find the velocity of the ball. (3 marks)
Ans. As per the question,
Mass of the ball = 5 kg
Linear momentum of the ball = 40 kgms-1.
Thus, after applying the Linear momentum formula, we can say:
p = m x v;
Now, since already know the linear momentum and mass of the ball, thus:
v = p / m
⇒ v = 30 / 5
⇒ 6ms-1 is the velocity of the ball.
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