Under which condition is the tension in a rope the same on both sides of a pulley?

Under which condition is the tension in a rope the same on both sides of a pulley?

• A. Frictionless Pulley
• B. Static Equilibrium for a Rigid Body
• C. Newton's Third Law
• D. Composite Bodies and External Source

Answer: (A)

With an ideal, frictionless pulley, the rope is free to slide without resistance and the pulley only redirects the rope. No friction means there’s no tangential force at the contact that would change the rope’s tension as it passes over the pulley, so the pulling force transmitted through the rope remains the same on both sides. If there were friction or the pulley had inertia (and thus needed to provide angular acceleration), the tensions would differ because the net torque on the pulley would require a difference in the side tensions.

With an ideal, frictionless pulley, the rope is free to slide without resistance and the pulley only redirects the rope. No friction means there’s no tangential force at the contact that would change the rope’s tension as it passes over the pulley, so the pulling force transmitted through the rope remains the same on both sides. If there were friction or the pulley had inertia (and thus needed to provide angular acceleration), the tensions would differ because the net torque on the pulley would require a difference in the side tensions.