First slide

Pure rotational motion and its kinetic energy

Question

A body spins about a fixed axis. If its angular velocity and angular momentum both are doubled, its kinetic energy

Moderate

A

increases by 300%
B

decreases by 150%
C

increases by 200%
D

decreases by 50%

Solution

$\begin{array}{l} K = \frac{1}{2} {Iω}^{2} = \frac{1}{2} (Iω) ω = \frac{1}{2} Lω \\ ∴ K^{1} = \frac{1}{2} L^{1} . ω^{1} = \frac{1}{2} (2 L) (2 ω) = 4 K \\ ∴ \frac{K^{1} - K}{K} \times 100 % = \frac{4 K - K}{K} \times 100 % = 300 % \end{array}$

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