Solving for Tension & Acceleration of Solid Cylinder

In summary, a uniform solid cylinder with a radius R and mass M is tied to a weightless rope, with one end attached to the ceiling of a building. When the cylinder is released, it falls towards the floor. The moment of inertia of the cylinder about an axis through its center of mass is given by I=0.5MR^2. To find the tension in the string, we need to solve for T. Additionally, to determine the acceleration of the cylinder, we need to solve for M.
  • #1
bluejay
4
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one end of a weightless rope is tied to the ceiling of a building and the other end is wrapped around a uniform solid cylinder that has a radius R and mass M. The cylinder is then released and falls toward the floor. The moment of inertia of a solid cylinder about an axis through its center of mass is: I=0.5MR^2

a.find the tension T in the string

b. what is the acceleration of M?
 
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  • #2
I haven't checked the rules of the forum for a while, but I don't think they've changed. You have to start showing us how you tried to solve the problem.
 

1. What is tension in a solid cylinder?

Tension in a solid cylinder refers to the force that is pulling or stretching the cylinder, typically caused by an external force acting on the object.

2. How is tension calculated in a solid cylinder?

Tension can be calculated in a solid cylinder by using the formula T = mg + ma, where T is the tension, m is the mass of the cylinder, g is the acceleration due to gravity, and a is the acceleration of the cylinder.

3. What is acceleration in a solid cylinder?

Acceleration in a solid cylinder refers to the rate of change of the cylinder's velocity. It is typically caused by an external force acting on the object.

4. How is acceleration calculated in a solid cylinder?

Acceleration in a solid cylinder can be calculated by using the formula a = (v - u)/t, where a is the acceleration, v is the final velocity, u is the initial velocity, and t is the time interval.

5. How are tension and acceleration related in a solid cylinder?

Tension and acceleration in a solid cylinder are related through the formula T = ma, where T is the tension, m is the mass of the cylinder, and a is the acceleration. This means that the tension in a solid cylinder will increase or decrease in proportion to the acceleration of the object.

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