posted by Kristen on .
A record turntable is rotating at 33 and 1/3 rev/min. A watermelon seed is on the turntable 7.5 from the axis of rotation
Calculate the acceleration of the seed assuming that it does not slip?
Suppose that the turntable achieves its angular speed by starting from rest and undergoing a constant angular acceleration for .75 seconds. Calculate the minimum coefficient of static friction required for the seed not to slip during the acceleration period?
I do not know if it is 7.5 nautical miles or what, so I will call the distance from the center r.
convert 33 1/3 rev/mi to radians/s
w = 33 1/3 rev/min *1 min/60 s *2 pi rad/rev
= 3.49 rad/s
a = w^2 r = 12.2 r
in units of length you are using/s^2
since I do not know your length unit I must leave g as g instead of 9.8 m/s^2 or 32 ft/s^2 or whatever
mu = friction coef
Now we also have a tangential friction problem because the table is accelerating
tangential acceleration = r*(change in w/change in time)
= r * ( 3.49 rad/s /.75 s)
= r * 4.65 length units/s^2
total acceleration = sqrt(tangenial^2 + radial^2)
= r sqrt (4.65^2 + 12.2^2)
= r sqrt (170)
= 13.0 r
Now friction force = m a
m g mu = m (13 r)
mu = 13 r/g