Question

The wizard has a mass of 80 kg and sits 3 m from the center of a rotating platform. Due to the rotation his speed is increased from rest by ˙ v = 0.4 m s 2 v˙=0.4ms2. If the coefficient of static friction between his clothes and the platform is μ s = 0.3 μs=0.3, determine the time requiredto cause him to slip.

Why do we equate the of both centroidal force and force in the radial direction to the friction force, but not
usR = mv^2/r?

Answer 1

You did not say what your acceleration was. I assume that you have both radial acceleration a= v^2/R and tangential acceleration (change in v/second).
They are perpendicular so needed friction force = m sqrt [ (v^2/R)^2 + (delta v/dt)^2 ]

Answer 2

Acceleration given as .4 m/s^2

Answer 3

then put in a = .4 m/s^2 starting at v (or more likely omega)0
I think you have typos, please check. Is it linear acceleration or angular? If angular then it is NOT m/s^2 but radians/s^2. What you gave me is gibberish.