Page 17 - 11-phy-5 Circular Motion

5. Circular Motion eLearn.Punjab

where q is the angle between r and p. The direction of L is For Your Information

perpendicular to the plane formed by r and p and its sense is
given by the right hand rule of vector product. SI unit of angular
momentum is kg m2s-1 or J s.

If the particle is moving in a circle of radius r with uniform angular

velocity w, then angle between r and tangential velocity is 90°.

Hence

But =L m=rv sin90o mrv The sphere in (a) is rotating in the sense
Hence v = rw given by the gold arrow. Its angular
velocity and angular momentum are
=L mr 2w taken to be upward along the rotational
axis, as shown by the right-hand rule
in (b).

Now consider a symmetric rigid body rotating about a fixed axis

through the centre of mass as shown in Fig 5.11. Each particle

of the rigid body rotates about the same axis in a circle with an

angular velocity w. The magnitude of the angular momentum

of the particle of mass mi is mi vi ri about the origin O. The

direction of Li is the same as that of w. Since vi = ri, w, the
angular momentum of the ith particle is mi ri2 w. Summing this

over all particles gives the total angular momentum of the

rigid body.

n Fig. 5.11

∑L = ( miri2 ) w = Iw
i=1

Where I is the moment of inertia of the rigid body about the axis of rotation.

Physicists usually make a distinction between spin angular momentum (Ls) and orbital angular
momentum (L0). The spin angular momentum is the angular momentum of a spinning body, while
orbital angular momentum is associated with the motion of a body along a circular path.

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