Physics20755 marksNumerical: rotating wheel with weightMoment of inertia and torque
A large wheel of radius 0.4 m and moment of inertia 1.2 mathrmkgm2, pivoted at the center, is free to rotate without friction. A rope is wound around it and a 2-kg weight is attached to the rope. When the weight has descended 1.5 m from its starting position (a) what is downward velocity? (b) what i
A large wheel of radius 0.4 m and moment of inertia 1.2 $\mathrm{kgm^2}$, pivoted at the center, is free to rotate without friction. A rope is wound around it and a 2-kg weight is attached to the rope. When the weight has descended 1.5 m from its starting position (a) what is downward velocity? (b) what is the rotational velocity of the wheel? [5]
Quantity Value ------ Radius of wheel, $r$ 0.4 m Moment of inertia, $I$ 1.2 kg·m² Mass of weight, $m$ 2 kg Distance descended, $h$ 1.5 m $g$ 9.8 m/s² Initial velocity 0 (starts from rest) --- The loss in gravitational PE equals the total gain in kinetic energy: $$mgh = \frac{1}{2}mv^2 + \frac{1}{...