What is the algebraic expression for the ratio ac,second/ac,minute of the centripetal accelerations for the tips of the second hand and the minute hand? Express your answer in terms of the periods Tsecond and Tminute. (Answer using T_m to be the period of the second hand and T_s to be period of the minute hand.)

Question

ac,second/ac,minute =

(d) What is the ratio ac,second/ac,minute of the centripetal accelerations for the tips of the second hand and the minute hand?
ac,second/ac,minute =

Answer 1

Let L be the length of a clock's hand and T be its period of rotation. The acceleration of the tip is
a = V^2/L = (2 pi L/T)^2/T = 4 pi^2 L^2/T

Note the inverse dependence upon T. If both hands had the same length L, the a of the second hand would be 60 times the a of the minute hand.

ac,second/ac,minute = T_minute/T_second = 60