Momentum of an object is the product of the velocity of the object and mass of the object. We sometimes refer to momentum of an object as a linear momentum. Linear momentum of an object is a vector quantity. There is another type of momentum called angular momentum which is a pseudovector quantity. This article on how to calculate momentum will help you in calculating both these momentums.
Calculating linear momentum:
Linear momentum of an object is a vector quantity since it has both magnitude and direction. The formula for calculating linear momentum is given as,
P = mv
In the above equation,
- P = momentum
- m = mass
- v = velocity
The SI unit for mass is kg and the SI unit for velocity is m/s, hence the SI unit for momentum is kg × m/s
- To calculate the momentum of the object, calculate the mass of the object which is under motion and calculate then velocity of the object using the formula for calculating velocity of the object ( velocity is the rate of change of displacement). Formula for calculating velocity is given as
Velocity = change of displacement/ time
- When you have calculated the velocity of the object and mass of the object place the calculated values in the above formula to calculate momentum of the object. This is the magnitude of the momentum of the object.
- Now, as momentum is a vector you need to know the direction of the momentum. The direction of the momentum is same as the direction of the velocity of the object.
Calculating angular momentum:
We called the angular momentum as a pseudovector because it only gains a flip when the rotation of the object is improper.
Angular momentum is sometimes termed as moment of momentum, rotational momentum. This can be used to describe the state of a particle which is under rotation.
Angular momentum is given by the formula:
L = rp = r × mv
This is the angular momentum of an object with respect to some arbitrary point of origin
In the above formula,
- L = angular momentum
- r = position of the particle form the origin
- p = mv = linear momentum
The angular momentum of a system of particle or the angular momentum of a rigid body is the sum of angular momentum of the individual particles in the body.
We can also compute the angular momentum of a rigid body rotating around an axis of rotation using the formula,
L = I ω
In this case, angular momentum is expressed as the product of the moment of inertia (MI) of the object and the angular velocity of the object. Moment of inertia of the object is the measure of the object’s resistance to the changes in the rotation.
In the above formula,
- L = angular momentum
- I = moment of inertia of the object
- “ω” is the angular velocity of the object under rotation
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