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Assume a uniform cylinder. A cord is wrapped around the cylinder (of mass m and radius r) as shown. The cylinder is released from rest. Find the velocity of the center of the cylinder after it has moved down a distance h. Hint: Assume IcyI = (1/2)mr^2 not mr^2, as shown in the back of the text. Solution Summing forces, m g - T = m a Summing torques, T r = I alpha As I = 1/2 m r^2, alpha = a / r, T r = 1/2 m r a T = 1/2 m a Plugging this into the sum of forces, m g - 1/2 m a = m a Solving for a, a = 2 g / 3 Using v^2 = vo^2 + 2 a h, and as vo = 0, then v = sqrt (4 g h /3) [ANSWER].

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Assume a uniform cylinder. A cord is wrapped around the cylinder (of mass m and radius r) as shown. The cylinder is released from rest. Find the velocity of the center of the cylinder after it has moved down a distance h. Hint: Assume IcyI = (1/2)mr^2 not mr^2, as shown in the back of the text. Solution Summing forces, m g - T = m a Summing torques, T r = I alpha As I = 1/2 m r^2, alpha = a / r, T r = 1/2 m r a T = 1/2 m a Plugging this into the sum of forces, m g - 1/2 m a = m a Solving for a, a = 2 g / 3 Using v^2 = vo^2 + 2 a h, and as vo = 0, then v = sqrt (4 g h /3) [ANSWER].

- 1. Assume a uniform cylinder. A cord is wrapped around the cylinder (of mass m and radius r) as shown. The cylinder is released from rest. Find the velocity of the center of the cylinder after it has moved down a distance h. Hint: Assume IcyI = (1/2)mr^2 not mr^2, as shown in the back of the text. Solution Summing forces, m g - T = m a Summing torques, T r = I alpha As I = 1/2 m r^2, alpha = a / r, T r = 1/2 m r a T = 1/2 m a Plugging this into the sum of forces, m g - 1/2 m a = m a Solving for a, a = 2 g / 3 Using v^2 = vo^2 + 2 a h, and as vo = 0, then v = sqrt (4 g h /3) [ANSWER]