Rotational Short Notes -II

Torque

τ=rXF

Also τ=Iα

Kinetic Energy is pure Rotating body
KE=(1/2)Iω2

Rotational Work Done

-If a force is acting on a rotating object for a tangential displacement of s = rθ (with θ being the angular displacement and r being the radius) and during which the force keeps a tangential direction and a constant magnitude of F, and with aconstant perpendicular distance r (the lever arm) to the axis of rotation, then the work done by the force is:

W=τθ

• W is positive if the torque τ and θ are of the same direction,
otherwise, it can be negative.

Power

P =dW/dt=τω


Angular Momentum

L=rXp
=rX(mv)
=m(rXv)

For a rigid body rotating about a fixed axis
L=Iω

dL/dt=τ

if τ=0 and L is constant

For rigid body having both translation motion and rotational motion

L=L1+L2

L1 is the angular momnetum of Center mass about an stationary axis
L2 is the angular momentum of the rigid body about Center of mass

Law of Conservation On Angular Momentum

If the external torque is zero on the system then Angular momentum remains contants

dL/dtext

if τext=0
then dL/dt=0


Equilibrium of a rigid body

Fnet=0 and τext=0



Angular Impulse:

∫τdt term is called angular impluse..It is basically the change in angular momentum


Pure rolling motion of sphere/cylinder/disc

-Relative velocity of the point of contact between the body and platform is zero
-Friction is responsible for pure rolling motion
-Friction is non disipative in nature

E = (1/2)mvcm2+(1/2)Iω2+mgh

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