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

1. 4π²MR²n²

2. 2π²MR²n²

3. π²MR²n²/2

4. 8π²MR²n²

View Answer

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

Question 2:

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

1. \[ \frac{L²}{K} \]

2. \[ \frac{L²}{2K} \]

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

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

View Answer

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

and

L = I ω ⇒ Substituting we get,

\[ I= \frac{L²}{2K} \]