A washing machine has a fast spin cycle of 542 rev/min and a slow spin cycle of 328 rev/min. The diameter of the washing machine drum is 0.43 m. What is the ratio of the centripetal accelerations for the spin cycles?
1 Answer
Explanation:
The equation for the centripetal acceleration
where

#R# is the radius of the circle of motion, which in this case is#(0.43"m")/2 = 0.215# #"m"# 
#T# is the time for one revolution, in#"s"# . To find this, we take the given untis of "revolutions per minute", convert it to "revolutions per second", and find the reciprocal of that (to get "seconds per revolution"):
#T_1 = ((542"rev")/(1cancel("min")))((1cancel("min"))/(60"s")) = 9.03"rev"/"s" = overbrace(0.111"s")^("reciprocal of"color(white)(x) 9.03)#
#T_2= ((328"rev")/(1cancel("min")))((1cancel("min"))/(60"s")) = 5.47"rev"/"s" = overbrace(0.183"s")^("reciprocal of"color(white)(x) 5.47)#
Plugging in the known values, we have, for each acceleration:
The ratio of the centripetal acceleration of the fastspeed setting to the lowspeed setting is thus
We can determine (from the equation) that the ratio is equal to the inverse of the square of the first time