# Pulley, Moment of inertia, and acceleration

1. Mar 29, 2005

### dalitwil

A mass of .375kg hangs from a string that is wrapped around the circumference of a pulley with the moment of inertia = .0125 kg*m^2 and a radius of .26m. When the mass is released, the mass accelerates downward and the pulley rotates about its axis as the string unwinds. What is the acceleration of the mass??

I have been using a=rF/mr^2, with my F=mg. The correct answer is 6.57m/s^2, but i can't seem to figure out why.

No rush on answering, the question is from a practice exam I am studying.

Thanks guys.

2. Mar 29, 2005

### xanthym

From the problem statement:
{String Tension} = S
{Mass of Suspended Entity} = m = (0.375 kg)
{Weight of Mass} = W = (0.375 kg)*(9.81 m/sec^2) = (3.6788 N)
{Cylinder Radius} = R = (0.26 m)
{Cylinder Moment of Inertia} = I = (0.0125 kg*m^2)

For the suspended entity:
{Net Force} = ma =
= W - S
::: ⇒ S = W - ma ::: Eq #1

For the cylinder:
{Net Torque} = Iα = I*a/R =
= S*R
::: ⇒ S = I*a/R^2 ::: Eq #2

Equating Eq #1 and Eq #2:
W - ma = I*a/R^2
::: ⇒ a = W/{m + I/R^2}
::: ⇒ a = (3.6788 N)/{(0.375 kg) + (0.0125 kg*m^2)/(0.26 m)^2}
::: ⇒ a = (6.5702 m/sec^2)

~~