What is the K.E of a 5 kg solid ball whose diameter is 15 cm if it rolls across a level surface with a speed of 2 m/s?

Solution

Theory: When the solid ball is rolling down on the surface, it posses kinetic energies due to its linear as well as rotational motions. Total kinetic energy of the ball is the sum of both these types of energies. Moreover, we know that in rotational motion, the moment of inertia, I, plays exactly the same role as the mass plays in linear motion. Another important thing to be noted is that for the solid ball, moment of inertia is

Given:

Mass of the solid ball = 5 Kg

Radius of ball = ½ (diameter) =7.5 cm=0.075 m

Linear velocity of the ball = 2 m/s

Required Kinetic Energy of the ball

Where ω is the angular velocity and can be determined by ω = v/r

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