Final answer:
The mass of the double pulley is calculated from its weight using the conversion between pounds and kilograms and considering gravitational acceleration. The torque depends on how the force is applied, and the moment of inertia depends on the given radius of gyration. Angular velocity would need specific conditions to be determined.
Step-by-step explanation:
The double pulley in question has a weight of 50 lb. To determine its mass, we can use the conversion factor where 1 lb is equivalent to approximately 0.453592 kg. Therefore, the mass (m) is calculated as m = weight / g, where g is the acceleration due to gravity (approximately 9.81 m/s2).
Torque (τ) is determined by the formula τ = r × F × sin(θ), where r is the lever arm radius, F is the force applied, and θ is the angle between the force vector and the lever arm. The torque in this case would depend on the specifics of how the force is applied to the pulley.
The moment of inertia (I) is given by the formula I = m × k02, where m is the mass of the object and k0 is the centroidal radius of gyration. Without the explicit value of k0, we cannot calculate the exact moment of inertia.
Angular velocity (ω) is the rate at which an object rotates about an axis and would be identified based on the specific circumstances in which the pulley is used, such as the rotational speed at which it is being driven or the angular displacement over time.