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How to find the Momentum from Velocity?

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  • Last Updated : 01 May, 2022

The velocity of an object is the rate of change of its position as a function of time and frame of reference. The speed is the same as the object’s speed and direction specifications (eg 20 km/h north). Velocity is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of objects. Velocity is a vector quantity. To define velocity we need both size and direction.. The scalar absolute value of a velocity is a coherently derived unit called velocity. S.I unit of velocity = meters per second (m/s). For a constant speed, an object must have a constant speed in a constant direction. A constant direction makes an object move in a straight path, so constant speed means moving in a straight line at a constant speed. 

Velocity is defined as the rate of change of position with respect to time and is also called instantaneous velocity to distinguish it from the average velocity. Some applications may require an average velocity of an object, i.e., a constant velocity that gives a variable velocity and a net displacement equal to a variable velocity in the same time interval v(t) for a period of time Δt.

The average speed can be calculated as v =  Δx/ Δt. ⇢ (i)

The average velocity is always less than or equal to the average velocity of the object. This can be done by recognizing that distance always increases strictly, but displacement can increase or decrease in magnitude as well as in direction.

Momentum

Momentum is typically the term allowed in sports. A team with momentum agrees and will try to stop. A team with a lot of impulsions is really going and it will be difficult to stop. It is a physical term. This indicates the number of movements with objects. The moving sports team is a pulse. If the object moves (on the move), there is an impulse. The pulse can be defined as “Mass in Motion”. All objects have mass. So, if the object moves, there is an impulse, which has its own movement. The amount of momentum with objects depends on the two variables. How many things move and how do materials move quickly? The momentum depends on variable mass and speed. For equations, the impact of the object is the same as the mass of the object time, which is the speed of the object.

Momentum = mass × velocity

p = mv ⇢ (ii)

Where, p refers to momentum and m and v are mass and velocity respectively.

The equation shows that momentum is directly proportional to the mass of an object and directly proportional to its velocity. The units of momentum are units of mass times units of velocity. The standard unit of momentum is kg.m/s. Although kg.m/s is the standard unit for momentum, there are many acceptable (though not generally accepted) units of momentum. Examples include kg.km/h, and g.cm/s. Here, the units of mass are multiplied by the units of velocity to get units of momentum. This is steady with the momentum equation.

Momentum is a vector quantity. Vector quantities are quantities that have magnitude and direction. To fully describe the momentum of a 10kg bowling ball moving westward at a speed of 4m/s, you must include information about both the size and direction of the bowling ball. It is not enough to say that the ball has an impact of 20 kg m/s. The momentum of the ball is not fully explained until information about its direction is provided. The direction of the momentum vector is the same as the direction of the ball’s velocity. The direction of the velocity vector coincides with the direction of movement of the object. If the bowling ball is moving in the west, its momentum can be sufficiently described as 20 kg.m/s in the west. As momentum is a vector quantity so an object is fully described in its magnitude and direction.

Momentum from velocity

As we can see in equation (ii) momentum is equal to the product of mass and velocity, it means if we have the information about velocity or we can say that we know the value of velocity we can calculate the momentum of any object or body. Momentum is of two kinds i.e., linear momentum and angular momentum,

Linear Momentum 

The linear momentum of an object is the product of its mass and velocity. Linear momentum is a vector quantity and the direction of momentum is considered to be the direction of the velocity of an object. If the mass of an object is m and the velocity of the object is {v}, then the linear momentum {p} is given by p= mv.

Linear momentum is a conserved quantity. A system is conserved when no external forces act on it. When the resulting external force acts on the system, the momentum is changed so that the rate of change of the momentum is equal to the resulting external force.

F = dp/dt.

The unit of measure for linear momentum in the kg m2 s-1.

Angular momentum 

For an object of mass m moving with velocity {v}, the angular momentum L with respect to the reference point is given by the cross product 

L = r × mv

Where r is the object’s position vector that describes the object’s position relative to the reference point. Since angular momentum is defined in terms of the cross product, the direction of the angular momentum vector is assumed to be perpendicular to both the particle’s position vector r and its velocity vector v.

L = Iω 

Where I is the moment of inertia and ω is the angular velocity. The unit of measure for angular momentum is kg m2 s-1.

Difference between Linear and Angular momentum

Linear MomentumAngular Momentum
It is the tendency of the mass of an object continues moving in a straight path.It is the tendency of the mass of an object to continue to rotate.
Linear momentum is parallel to v.It is perpendicular to both v and r. 
It is a vector and conserved quantity.It is a vector and conserved quantity.
Magnitude is the mass times its speed.Magnitude is the rotational mass times its angular speed.
There is a net force required to change it.There is net torque required to change it.
If the mass is greater means that greater force is needed to change the momentum.If the moment of inertia is greater means that greater the torque is needed to change the momentum.

Sample Questions

Question 1: Determine the momentum if a ball is blowing in westward at 9m/s having a mass of ball 60 Kg.

Solution: 

Given, mass(m) = 60 Kg and velocity (v) =9m/s.

Momentum = mass × velocity

p = mv

p = 60 × 9

p = 540Kg m/s, west.

Question 2: A car of mass 1200Kg moving with the speed of 3m/s in an eastward direction. Calculate its momentum.

Solution: 

Given, Mass of a car (m) = 1200Kg, velocity(v) = 3m/s.

Using formula of momentum, p = mv

p = 1200 × 3

p = 3600 Kg m/s, east.

Question 3: A moving object possesses a momentum of 20,000 units. If its velocity will be doubled then what would be its new momentum?

Solution:

Given that momentum is 20,000 units, As p = mv. 

Here momentum is directly proportional to velocity.

When doubling the velocity, will double the momentum so the new momentum is 40,000 units.

Question 4: A bullet of mass 0.2 Kg moving with a velocity of 500 m/s. Find its momentum.

Solution:

Mass of Bullet (m) = 0.2 Kg and velocity of bullet (v) = 500m/s.

p = mv

p = 500 × 0.2

p =100 Kg m/s.

Question 5: A ball has a momentum of 50 Kg m/s having a mass of 10 Kg. Calculate the velocity of the ball.

Solution:

Given, Mass(m) = 10 Kg and Momentum(p) =  50 Kg m/s.

p = mv

v = p/m

v = 50/10

p = 5 m/s.

Question 6: What will be the momentum of a stone if it is thrown at the velocity of 3 m/s and has a mass of 8 Kg?

Solution:

Velocity (v) = 3m/s  and mass = 8Kg.

According to the formula of momentum, p = mv

So, p = 8×3

p = 24 Kg m/s.

Question 7: What is the momentum of a 60 Kg of motorbike moving with a velocity of 40 m/s?

Solution:

Given information, Mass(m) = 60Kg and velocity (v) = 40m/s.

Momentum, p = mv

p = 60 × 40

p = 2400 Kg m/s.

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