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1. The problem statement, all variables and given/known data

A cylinder with a moment of inertia I (about its axis of symmetry), mass m, and radius r has a massless string wrapped around it which is tied to the ceiling (Intro 1 figure) .

At time t=0 the cylinder is released from rest at height h above the ground. Use g for the magnitude of the acceleration of gravity. Assume that the string does not slip on the cylinder. Let v_vec represent the instantaneous velocity of the center of mass of the cylinder, and let omega_vec represent the instantaneous angular velocity of the cylinder about its center of mass. Note that there are no horizontal forces present, so for this problem

v_vec = -v(y-hat) and omega_vec = - omega(z-hat)

2. Relevant equations

Torque = I(angular_acceleration)

F= m(linear_acceleration)

3. The attempt at a solution

I'm having trouble with part B

T is the tension of the spring

if I goes to zero, the object will be turning faster in the -z direction.

The tension of the spring does less work on its rotation and more work on its linear momentum.

and so

If the T went to 0, then linear a should be g right?

because the tension does no work on either the angular and linear momentum and so the cylinder will just fall right?

the answer is the second choice

right?

if T went to infinity, then there would not be acceleration in the in the -y direction.

so if T went to infinity, a should be zero right?

if T equaled mg then linear acceleration would also be zero because the forces of the weight and T cancel out

right?

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# Homework Help: Unwinding Cylinder-Dynamics

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