Question 7.12:
A
solid cylinder of mass 20 kg rotates about its axis with angular
speed 100 rad
s–1.
The radius of the cylinder is 0.25 m. What is the kinetic energy
associated with the rotation of the cylinder? What is the magnitude
of angular momentum of the cylinder about its axis?
Solution:
Mass
of the cylinder, m
= 20 kgAngular speed, ω = 100 rad s–1
Radius of the cylinder, r = 0.25 m
The moment of inertia of the solid cylinder:
I = mr2 / 2
= (1/2) X 20 X (0.25)2
= 0.625 kg m2
∴ Kinetic energy = (1/2) I ω2
= (1/2) X 6.25 X (100)2 = 3125 J
∴Angular momentum, L = Iω
= 6.25 × 100
= 62.5 Js
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