A uniform rod of mass 300 g and length 50 cm rotates at a uniform angular speed of 2 rad/s about an axis perpendicular to the rod through an end. Calculate (a) the angular momentum of the rod about the axis of rotation, (b) the speed of the centre of the rod and (c) its kinetic energy.
(a) the angular momentum of the rod about the axis of rotation is 0.05 kg-m2/s
(b) the speed of the center of rod and is 50 cm/s
(c) the kinetic energy is 0.05 J
Given
A uniform rod of length 50 cm and mass 300g is rotating under uniform angular speed of 2 rad/sec about its axis.
Formula used
The formula used to find the angular momentum of the rod is the product of the momentum of Inertia and angular velocity. In second part the speed of the rotation of the rod is equivalent to the product of the angular velocity and the distance from the end of the rotating point of the object. And lastly, the kinetic energy which is calculated as given in the Formula below,
&
&
where,
L is the momentum, I is the moment of Inertia, 
is average. velocity, r is radius of rotation and K.E. is kinetic energy.
Explanation
(a) The average momentum is
The value of I of the rod is given as
Hence, average momentum is
(b) Speed of the center of rod is
(c) The kinetic energy generated is
