Question

A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s^-1. The radius of the cylinder is 0.25 m. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?

Answer 1

Given

• Mass of cylinder: \( m = 20 \,\text{kg} \)
• Radius of cylinder: \( R = 0.25 \,\text{m} \)
• Angular speed: \( \omega = 100 \,\text{rad s}^{-1} \)
• Solid cylinder rotating about its own axis.

1. Moment of Inertia of a Solid Cylinder

About its axis: \[ I = \frac{1}{2} m R^{2} \] Substitute: \[ I = \frac{1}{2} \times 20 \times (0.25)^{2} = 10 \times 0.0625 = 0.625 \,\text{kg m}^{2} \]

2. Rotational Kinetic Energy

\[ K = \frac{1}{2} I \omega^{2} \] \[ K = \frac{1}{2} \times 0.625 \times (100)^{2} = 0.3125 \times 10000 = 3125 \,\text{J} \]

3. Angular Momentum

\[ L = I \omega \] \[ L = 0.625 \times 100 = 62.5 \,\text{kg m}^{2} \text{ s}^{-1} \]

Final Answers

• Rotational kinetic energy: \[ \boxed{K = 3125 \,\text{J}} \]
• Angular momentum: \[ \boxed{L = 62.5 \,\text{kg m}^{2} \text{ s}^{-1}} \]