Assume a uniform cylinder. A cord is wrapped around the cylinder (of .pdf
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].
Assume a uniform cylinder. A cord is wrapped around the cylinder (of .pdf
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].
![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]](https://image.slidesharecdn.com/assumeauniformcylinder-230324063415-213400b5/75/assume-a-uniform-cylinder-a-cord-is-wrapped-around-the-cylinder-of-pdf-1-2048.jpg?cb=1679641113)
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Assume a uniform cylinder. A cord is wrapped around the cylinder (of .pdf
- 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]