Rotational Kinetic Energy – Rankers Physics

Rotational Kinetic Energy

Question 1:
A circular ring of wire of mass M and radius R is making n revolutions/sec about an axis passing through a point on its rim and perpendicular to its plane. The kinetic energy of rotation of the ring is given by

4π²MR²n²

2π²MR²n²

π²MR²n²/2

8π²MR²n²

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Solution:

Rotational Kinetic Energy = ½ I ω²= ½(2MR²)(2πn)²= 4π²MR²n²

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Question 2:
What is moment of inertia in terms of angular momentum (L) and kinetic energy (K)

\[ \frac{L²}{K} \]

\[ \frac{L²}{2K} \]

\[ \frac{L}{2K^{2}} \]

\[ \frac{L}{2K} \]

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Solution:

\[ K = \frac{1}{2}I \omega^{2} \]

and

L = I ω ⇒ Substituting we get,

\[ I= \frac{L²}{2K} \]

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