1. Moment of Inertia (I)
* Formula: I = mk², where:
* m = mass of the rope (6 kg)
* k = radius of gyration (40 cm = 0.4 m)
* Calculation: I = (6 kg) * (0.4 m)² = 0.96 kg·m²
2. Rotational Kinetic Energy (KE_rot)
* Formula: KE_rot = (1/2) * I * ω² , where:
* I = moment of inertia (0.96 kg·m²)
* ω = angular velocity (convert rpm to rad/s)
* Convert rpm to rad/s:
* ω = (300 rpm) * (2π rad/1 rev) * (1 min/60 s) = 10π rad/s
* Calculation: KE_rot = (1/2) * (0.96 kg·m²) * (10π rad/s)² ≈ 471.24 J
Therefore:
* Moment of Inertia (I): 0.96 kg·m²
* Rotational Kinetic Energy (KE_rot): 471.24 J (approximately)
