Linear and angular momentum

This ppt describes linear and angular momentum of rigid body.

1. Linear and Angular Momentum C.D. Mungmode M. G. College, Armori

2. Linear Momentum: When particle with mass m moves with velocity v , we define its Linear Momentum p as product of its mass m and its velocity v: Unit of linear momentum is kg m / s. There is no special name for this unit. It is the measure of how hard it is to stop or turn a moving object.

3. Conservation of Linear Momentum: Consider a system of particles. The total linear momentum of a system of particles is constant whenever the vector sum of the external forces on the system is zero and subjected to their mutual interaction. In particular, the total momentum of an isolated system is constant. If Σ F ext = 0, then ΔP = 0, so P = constant, and in any instant of time P1 = P2

4. Angular Momentum: Consider a point-like particle of mass m moving with a velocity v . The linear momentum of the particle is p = m v . Consider a point S located anywhere in space. Let r denote the vector from the point S to the location of the object. Define the angular momentum J̅ about the point S of a point-like particle as the vector product of the vector from the point S to the location of the object with the linear momentum of the particle, It is also defined as moment of its linear momentum about a fixed point.

5. The derived SI units for angular momentum are [kg ⋅m2 ⋅s−1] = [ N⋅m⋅s ] = [J ⋅s]. There is no special name for this set of units. It is a vector quantity. Its direction is perpendicular to both r and p. The magnitude of it can also be written as

6. Angular Momentum of a Rigid Body: The sum of the moments of the linear momentum of all the particles of a rotating rigid body about the axis of rotation is called its angular momentum. Consider the particles of mass m 1 , m 2 , ..... of the rigid body lying at distance r 1 , r 2 , .... from the axis of rotation having linear velocities v 1 , v 2 , .... Respectively. ω is the magnitude of angular velocity, then Linear momentum of particle m 1 = m 1 v 1 = m 1 r 1 ω Hence, angular momentum of particle m 1 = m 1 v 1 r 1 = m 1 r 1 2 ω Similarly, for second particle of mass m 2 , angular momentum is = m 2 r 2 2 ω Therefore, angular momentum of all the particles = m 1 r 1 2 ω + m 2 r 2 2 ω + ..... J = Σ mr 2 ω = I ω Where, I = Σ mr 2 is moment of inertia of rigid body.

7. Torque: If a force F acts on a particle at a point P whose position with respect to the origin O is given by displacement vector r, the torque τ on the particle with respect to origin O is defined as, τ = r x F