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.
How to find the Momentum from Velocity?
We can find momentum from velocity by multiplying it with mass i.e. Momentum = mass × velocity. Momentum is a vector quantity in physics that is a property of motion and is obtained by calculating the product of mass and velocity. Momentum always remains conserved in a closed space.
Velocity is defined as the rate of change of position as a function of time and frame of reference 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 some time Δt.
The average speed can be calculated as v = Δx/ Δt.
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.