Aplatform is free to rotate in the horizontal plane about a frictionless, vertical axle. about this axle the platform has a moment of inertia ip. an object is placed on a platform a distance r from the center of the axle. the mass of the object is m and it is very small in size. the coefficient of friction between the object and the platform is μ. if at t = 0 a torque of constant magnitude τ0 about the axle is applied to the platform when will the object start to slip?

It will start to slip at

Explanation:

We can find the angular acceleration from a sum of torque on the system:

 Solving for α

Now, on the object, we make a sum of forces on the centripetal-axis:

  Solving for ω:

From a sum of forces on the axis perpendicular to the platform:

Replacing this value into the ω equation:

 Now we have to find the amount of time that takes to the object to get this speed.

  Solving for t:

grav potential energy

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west