- #1

- 178

- 0

## Homework Statement

A washing machine's two spin cycles are 328 rev/min and 542 rev/min. The diameter of the drum is 0.43 m.

What is the ratio of the centripetal accelerations for the fast and slow spin cycles?

## Homework Equations

a

_{c}=v

^{2}/r

linear velocity: v=rw (w is really omega)

angular velocity= change in theta/change in time

I think that's all I need.

## The Attempt at a Solution

First I changed the angular velocities from rev/min to rad/s. So, 328 rev/min=34 rad/s, and 542 rev/min=57 rad/s.

I solved for the slow cycle's acceleration first. Since it is in linear velocity instead of angular velocity, i solved for the linear velocities for the slow and fast cycle.

v=rw -> v

_{s}=(.215 m)(34 rad/s) -> 7.31 m/s

v=rw -> v

_{f}=(.215 m)(57 rad/s) -> 12.3 m/s

Then I plugged these into the centripetal acceleration formula for the slow and fast cycles.

a

_{cs}=v

^{2}/r -> a=(7.31 m/s)(7.31 m/s)/(.215 m) -> 248.54 m/s

^{2}

a

_{cf}=v

^{2}/r -> a=(12.3 m/s)(12.3 m/s)/(.215 m) -> 703.67 m/s

^{2}

There may not be anything wrong with it, but those numbers for the acceleration seem soooooo big. It's easy physics, so I don't know what I'm doing wrong. >:(

Last edited: