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?
(angular_momentum) 62.5 kg m² s⁻¹
(kinetic_energy) 3125 J
Explanation
This numerical problem requires calculating rotational kinetic energy and angular momentum. The context provides the kinetic energy formula K = ½Iω² (Eq. 6.35) and establishes that moment of inertia I is the rotational analogue of mass. For a solid cylinder rotating about its axis, the moment of inertia is I = ½MR² (from Table 6.1 referenced in context). Angular momentum L = Iω follows from the rotational-linear motion analogy discussed in the context.
Solution Steps
Step 1: Identify given values - Mass M = 20 kg, Angular speed ω = 100 rad s⁻¹, Radius R = 0.25 m
Step 2: Calculate moment of inertia - For solid cylinder about its axis: I = ½MR² = ½ × 20 × (0.25)² = ½ × = 0.625 kg m²
Step 3: Calculate rotational kinetic energy - K = ½Iω² = ½ × 0.625 × (100)² = ½ × = 3125 J
Step 4: Calculate angular momentum - L = Iω = = 62.5 kg m² s⁻¹