Work, Energy and Power for Rotating Body

1. Work : If the body is initially at rest and angular displacement is dθ due to torque then work done on the body.

              W = ∫τdθ                              [Analogue to work in translatory motion W =  ∫Fdx]

2. Kinetic energy : The energy, which a body has by virtue of its rotational motion is called rotational kinetic energy. A body rotating about a fixed axis possesses kinetic energy because its constituent particles are in motion, even though the body as a whole remains in place.

Rotational kinetic energy	Analogue to translatory kinetic energy
KR= ½ Iω2	KT= ½ mv2
KR= ½ Lω	KT= ½ Pv
KR= (L2/2I)	KT= (P2/2m)

3. Power : Rate of change of kinetic energy is defined as power

P = (d/dt) (K_R) = (d/dt) [ ½ Iω²]= Iω (dω/dt) = Iωd = Iαω = τω

In vector form Power                                 [Analogue to power in translatory motion  ]