calculate the Kinetic energy of a uniform circular disc of mass 100 gram and diameter 10 cm making 100 revolution per minutes with respect to its axis
Answers
Answer :
The K.E = 7.81 × 10^-10 J
Step-by-step Explanation :
Given : Mass of disc = 100 gm = 0.1 kg
Diameter of Disc = 10 cm ( radius = 10/2 = 5cm = 0.05 metre )
Angular velocity = 100 r.p.m = 10.47 rad/s
To find : Kinetic Energy = ?
We know that,
Kinetic Energy = 1/2 × I × ω²
Where,
I = Moment of Inertia
= 1/2 × M × R² ----------- ( for circular Disc )
= 1/2 × 0.1 × (0.05)²
= 0.000125
= 1.25 × 10^-4
ω = angular velocity
Substituting the given value in above formula we get,
K.E = 1/2 × (1.25 × 10^-4)² × 0.1
= 1/2 × 1.563 × 10^-8 × 0.1
= 0.07815 × 10^-8
= 7.81 × 10^-10 J