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:

as we know our atmosphere or air have different levels. every level has other gasses, and every gas has another permeability. when the light comes from lower permeability to higher permeability, it changes its direction. so that means that when the light comes from the moon to the earth, it changes it's direction many more times. it basically means that the shape of the light part of the moon is changed on the earth.

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