When a body has mass, it moves along a straight line. Then it is defined as its momentum.
Let us know, Is Momentum A Vector Quantity:- Newton’s second law of motion states that the rate of change of momentum of a body is directly proportional to the applied force, and this change takes place in the direction of the applied force.
From Newton’s second law, we understand that if a constant force is applied to a particle for a given period, the product of force and the time interval are equal to the change in the momentum. Contrariwise, the momentum of a body is defined as the time required to bring it to rest by a constant force.
Why is momentum a vector quantity
The product of mass and velocity, which is the momentum of a body, is a vector quantity because the direction of the body in motion will be in the direction same to the direction of the velocity of the body having mass. Where we know that quantities like displacement, position, velocity, force, and torque, these quantities have both magnitude and direction are vector quantities or vectors.
And we also know that quantities like mass, length, volume, Time, temperature, distance, and energy have magnitude only. They do not have directions are called scalar quantities or scalars.
Is linear momentum a vector quantity
Linear momentum is the product of mass, and the velocity of a body as its direction will be in the motion of velocity.
Linear momentum is a vector quantity, and it is represented by
Let us consider a body having mass and its velocity be then we get:-
Let us understand momentum and how it is a vector quantity:-
Suppose a bus has mass M1 and a truck has mass M2 (M2 greater than M1) in motion having the same velocities V moving in east. now their momentum will be P1 and P2, respectively.
So now we can write the equation as,
As we know, M2 is greater than m1, so P2 will be greater than P1. This means a body with a higher body mass will have large momentum than a body with light body mass.
Here the momentum is a vector quantity which means the bus and truck will move in the east direction.
Now lets us consider a bus of mass M1 and a truck of mass M2. Both are moving with the velocity of V1 in the east and V2 moving in the west, respectively, having the same linear momentum.
Now the equation can be written as:-
Here M2 is greater than M1, and V2 is greater than V1.
This means a heavier body has a smaller velocity, and a lighter body has a higher velocity.
Here we know momentum is the vector which means the bus will move in the east direction as its velocity directs, and the truck will move in the west direction as its velocity directs.
Is angular momentum a vector quantity
Angular momentum can be understood as the quantity corresponding to linear momentum in a rotational motion.
Let us understand angular momentum and whether it is a vector quantity:-
To understand angular momentum as a vector quantity, Let’s think about a particle with mass ”M,” And its linear momentum is given as, which it is at a position which is relative to the origin O.
Here the angular momentum of the particle will be:-
The angular momentum will also be vector quantity, whose direction will be decided through the right-hand screw rule.
The magnitude of angular momentum will be given as,
Where is the angle between
We need to note that angular momentum will be 0 if the linear momentum is not there. Or, if the particle will be at the origin, which means R will be 0, or the directional line passes through the origin, the angular momentum will be 0.
From the above discussion, we got to know that angular momentum is a vector quantity. And from the right-hand screw rule, its direction is determined to be at right angles to the plane,
However, we need to note that the angular momentum of a particle or a system is due to the linear momentum transverse component. This means there is no contribution of the radial component.
Problems based on momentum
Q. Consider a toy train having a mass of 18 kg moving with a velocity of 8 m/s toward the south. What will be the momentum of the toy train?
We know that the momentum of the body will be:-
Where m is 18 kg and v is 8 m/s
So the momentum of the toy train will be
Q. There are Two trains of equal mass (2200 kg) that are moving at a speed of speed (72 km/h). The two trains collide head-on in a completely inelastic collision. Now, find out the vector sum of the momentum of the system of two trains after the collision?
The specified circumstance is an instance of an inelastic collision.
In these collisions, the kinetic energy will not get conserved (this means that it will be converted into some other form of energy, for example, heat energy ). However, the momentum will get conserved in any condition, whether it is an elastic collision or inelastic collision. And, as discussed above, momentum is a vector which means it has direction. Since the trains were of equal mass and traveled towards each other at the same speed as they collided, we know their momentum was equal in magnitude and opposite direction. This means the sum of their vector momentum before the collision will be 0.
Q.1-kg ball moves at speed of4 m/s. Now the ball is hit by an opposite force, F. This causes the speed of the ball to change to 12 m/s. The ball was in contact with the batsman for 0.02 seconds. Calculate the change in momentum of the ball.
From the above figures, we know that,
Mass of ball (m) = 1kg
Initial velocity (vo) = 4 m/s
Final velocity (vt) = -12 m/s
Time interval (t) = 0.02 second
Now to calculate the change, the given equation will be:-
∆p = m vt – m vo = m (vt – vo)
∆p = (1kg)(- 12 m/s – 4 m/s)
∆p = (1 kg)(-16)
∆p = 16kg m/s