# Calculate Maximum Velocity with Swing Chain Length and Angle

• drobtj2

## Homework Statement

Using the length of a swing's chain (1.8m) and using the angle the swing starts at relative to the vertical (30 deg.) devise a method to calculate the max veloc. of the swing at the bottom. Assume mass of person+swing=72 kg

Ui+Ki=Uf+Kf
K=1/2 mv^2
U=mgh
h= 1.8 cos 30
Krot= 1/2 Iw^2

## The Attempt at a Solution

(m)(9.8)(.24)=1/2 m v^2 +1/2 Iw^2
2.35= 1/2 v^2+ 1/2 r^2 (v^2/r^2)
2.35= 1/2 v^2 + 1/2 v^2
2.35=v^2
v=1.53 m/s

Do I use the rotational kinetic energy when solving the problem? It seems like I should because of the rotational motion but I'm not sure.

you can use rotational energy, altough it's not really necessary since all the mass is in one point and all the forces act on this point.
you can't use BOTH howvever. The rotational energy of the swinger is the same energy as the ordinary kinetic energy.

Thanks, this problem was part of a lab, and later the experimental and theoretical data didnt match, so i figured my method had been wrong, and I got good results using only kinetic.