Question

A very light cotton tape is wrapped around the outside surface of a uniform cylinder of mass M and radius R. The free end of the tape is attached to the ceiling. The cylinder is released form rest and as it descends it unravels from the tape without slipping. The moment of inertia of the cylinder about its center is I = 1/2 MR2

a. On the diagram above show all the forces applied on the cylinder. b. Find the acceleration of the center of the cylinder when it moves down. c. Find the tension force in the tape.

Answer 1

Answer:

Explanation:

Check attachment for answer.

Answer 2

The acceleration of the center of the cylinder and the tension force in the tape is mathematically given as

a=2g/3

T=ug/3

What are the forces applied on the cylinder, the acceleration of the center of the cylinder when it moves down, and the tension force in the tape?

Generally, the equation for the Liner motion  is mathematically given as

Mg-T=Ma

Therefore

Mg.R=(0.5MR^2+MR^2)\alpha

$\alpha=2g/3R$

b)

Where

a=\alpha R

Hence

a=2g/3

c)

For the tension T

ug-T=Ma

T=u(g-a)

T=ug/3

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