Torque on a Couple of Pulleys?

📌 CONCEPT: A couple of pulleys is a system of two pulleys that allows a force to be applied at a distance from the load, resulting in a torque that causes the load to rotate.

📐 RULE / FORMULA: The torque on the load is given by τ = r × F, where τ is the torque, r is the radius of the pulley, and F is the force applied to the pulley.

💡 WORKED EXAMPLE: Given that the force applied to the first pulley is 20 N and the radius of the pulley is 5 cm, we can calculate the torque on the load. Using the formula τ = r × F, we get τ = 0.05 m × 20 N = 1 Nm. Since the load is lifted at a constant rate, the torque is also constant, and we can use the formula τ = I × α to find the angular acceleration α. However, we are not given the moment of inertia I, so we need to use the fact that the load is lifted at a constant rate of 1 m/s^2 to find the angular acceleration.

⚠️ COMMON MISTAKE: Students may forget to consider the radius of the pulley when calculating the torque, or they may assume that the torque is zero since the force is applied horizontally.