The solid right-circular cylinder of mass 500 kg is set into torque-free motion with its symmetry axis initially aligned with the fixed spatial line a–a. due to an injection error, the vehicle’s angular velocity vector ω is misaligned 5◦ (the wobble angle) from the symmetry axis. calculate to three significant figures the maximum angle φ between fixed line a–a and the axis of the cylinder.

30.95°

Explanation:

We need to define the moment of inertia of cylinder but in terms of mass, that equation say,

Replacing the values we have,

At the same time we can calculate the mass moment of intertia of cylinder but in an axial way, that is,

Finally we need to find the required angle between the fixed line a-a (I attached an image )

Replacing the values that we have,

what is the actual question though?

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .