# Equilibrium

by • 04/07/2012 • GeneralComments (0)610

## Equilibrium

A body is said to be in equilibrium if it is

1. At rest, or

2. Moving with uniform velocity

A body in equilibrium possess no acceleration.
Static Equilibrium

The equilibrium of bodies at rest is called static equilibrium. For example,

1. A book lying on a table

2. A block hung from a string
Dynamic Equilibrium

The equilibrium of bodies moving with uniform velocity is called dynamic equilibrium. For example,

1. The jumping of a paratrooper by a parachute is an example of uniform motion. In this case, weight is balanced by the reaction of the air on the parachute acts in the vertically upward direction.

2. The motion of a small steel ball through a viscous liquid. Initially the ball has acceleration but after covering a certain distance, its velocity becomes uniform because weight of the ball is balanced by upward thrust and viscous force of the liquid. Therefore, ball is in dynamic equilibrium.
Angular Momentum

Definition

The quantity of rotational motion in a body is called its angular momentum. Thus angular momentum plays same role in rotational motion as played by linear momentum in translational motion.

Mathematically, angular momentum is the cross-product of position vector and the linear momentum, both measured in an inertial frame of reference.

ρ = r x P
Explanation

Consider a mass ‘m’ rotating anti-clockwise in an inertial frame of reference. At any point, let P be the linear momentum and r be the position vector.

ρ = r x P

ρ = r P sinθ ……….. (magnitude)

ρ = r m V sinθ ………. {since P = m v)

where,

V is linear speed

θ is the angle between r and P

θ = 90º in circular motion (special case)

The direction of the angular momentum can be determined by the Righ-Hand Rule.

Also

ρ = r m (r ω) sin θ

ρ = m r2 ω sin θ
Units of Angular Momentum

The units of angular momentum in S.I system are kgm2/s or Js.

1. ρ = r m V sin θ

= m x kg x m/s

= kg.m2/s
2. ρ = r P sin θ

= m x Ns

= (Nm) x s

= J.s

Dimensions of Angular Momentum

[ρ] = [r] [P]

= [r] [m] [V]

= L . M . L/T

= L2 M T-1