- #1

Wellesley

- 274

- 3

**Rotational Motion Find g - Galileo Inclined Plane**

## Homework Statement

Galileo measured the acceleration of gravity by rolling a sphere down an inclined plane. Suppose that, starting from rest, a

**sphere takes 1.6s**to roll a distance d

**istance of 3.00 m down a 20 degree inclined plane**. What value of

*g*can you deduce from this?

## Homework Equations

PE=KE(trans.)+KE (rot.)

I=2/5Mr^2

torque=force*distance

Torque=I*angular acceleration

## The Attempt at a Solution

-I've tried to use torque to solve for the acceleration down the plane, and this yielded a=5/7 * g *sin (theta)

I used:

distance=1/2at^2 to solve for a.

a=2.34375m/s^2

When this is plugged back in, I get:

2.34375=5/7 * g *sin (theta)

(2.34375*7)/5=3.28125

3.28125/sin(20)=9.59373

g= 9.59373 m/s

^{2}

[STRIKE]This is not close to the answer of 9.6, or the accepted value (9.81). I know I'm doing something significantly wrong, but I can't figure out exactly what the problem is. If anyone could point me in the right direction, I'd really appreciate it. Thanks.[/STRIKE]

The original problem had to do with an incorrect interpretation of the parallel-axis theorem. It should have been I=I

_{CM}+md

^{2}.

Last edited: