Looking for classes? Ksquare Career Institute, Bengaluru →
System of Particles and Rotational Motion
Kinetic Energy of Rolling Motion
1 question from 1 paper, each with its answer.
- question
- 1
- paper
- 1
- of System of Particles and Rotational Motion
- 1%
Concepts tested
- Fraction of rotational kinetic energy
All Questions
2003 AIPMT 1 question
-
A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is K. If radius of the ball be R, then the fraction of total energy associated with its rotational energy will be :For rolling without slipping, $v = R\omega$ and $I = mK^2$.
Total kinetic energy: $T.K.E. = \dfrac{1}{2}mv^2 + \dfrac{1}{2}I\omega^2 = \dfrac{1}{2}mv^2\left(1 + \dfrac{K^2}{R^2}\right)$
Rotational kinetic energy: $R.K.E. = \dfrac{1}{2}I\omega^2 = \dfrac{1}{2}mK^2\dfrac{v^2}{R^2} = \dfrac{1}{2}mv^2\left(\dfrac{K^2}{R^2}\right)$
Fraction $= \dfrac{R.K.E.}{T.K.E.} = \dfrac{K^2/R^2}{1 + K^2/R^2} = \dfrac{K^2}{K^2 + R^2}$
