1. Motion, Forces and Energy Torque, Angular Momentum and Its Conservation
Fsinf
The tendency of a force to rotate an
object about some axis is called TORQUE.
Torque is defined as t = F sin f r r f
Fcosf z F1
Line of action d d1 O d2
In the figure to the right, there are two forces
Acting in opposite senses. One (F1) causes
Anti-clockwise rotation, the other clockwise.
Net torque about O-axis, t = F1d1 – F2d2 F2

2. Torque and angular accelerationy
dFt
For any element dm, we know from Newton’s
2nd Law that dFt = (dm) at where at is the tang-
ential acceleration. dm r q x O
The torque dt = r dFt = (r dm) at
From earlier we saw that at = r a
So we can write:
dt = (r2dm)a
The net torque is given by:
This is the rotational analogue of Newton’s 2nd Law, F = ma

3. Angular Momentum and Its Conservationx y z vi mi r
We can find the angular momentum
of this disk by considering each mass
element, mi.
Differentiating gives:
The net external torque acting on a rigid object rotating about a fixed axis is equal
to the moment of inertia about the rotation axis multiplied by the object’s angular
acceleration.

4. Conservation of Angular Momentum
The total angular momentum of a system is
Constant if the resultant external torque acting
On the system is zero: Stext = dL / dt = 0 M
OR/ Angular momentum before a redistribution
of mass is equal to the angular momentum after
such a redistribution. R1 R2
Therefore if we know M, m, R1, R2 and w1, then
we can find w2.
Man walks inwards from
R1 to R2.