# Rotational Motion FInding the total ENergy

1. Aug 12, 2004

### Schu

Particulars:
ball has a radius of 2.5 cm a mass of .125 and is rolling across a table with a speed of .547 m/s, this table is 1.04 m off the ground. It rolls to the edge and down a ramp How fast will it be rolling across the floor?

First I found the Gravitational Potential Energy: Ep=mgh
Initial of 1.2753 FInal = 0

THen the Linear Kinetic ENergy : 1/2 mv^2
Initial .0187005625 FInal .0625v^2

Elastic Potential Energy: .5k(delta)x^2
0 0

Rotational Kinetic Energy: 1/5mv^2
initial .007480225 FInal .025v^2

Now I need to bring them all togther and solve the final velocity.

Is the Sum of the inital energy's = to the SUM of the final energy's?
If that's true then 1.30148075 = .0875v^2
so v = 3.85 m/s
Is that at all right??

2. Aug 12, 2004

### Schu

I need help ASAP

Is anyone out there????

I would appreciate the help

3. Aug 13, 2004

### Galileo

Looks ok to me. (I got 3.86 m/s, by rounding off)

4. Aug 13, 2004

### Staff: Mentor

rotational KE

The rotational KE is ${KE}_{rot} = 1/2 I \omega^2$.
You will also need the "rolling condition": $V = \omega R$.