Answer:
I = M*(0.5R^2 + h^2)
w = sqrt [2*g*h / (0.5R^2 + h^2)]
Explanation:
Given:
- The radius of the cylinder R
- The mass of the cylinder M
- The distance between horizontal axis h
- The moment of inertia of cylinder I_c
Solution:
- When the axis of rotation and axis with respect to rotation inertia is required do not coincide then we have to apply parallel axis theorem to calculate the moment of inertia about the required axis which is at a distance h from body rotational axis as follows:
I = I_c + M*h^2
- Where I_c of a cylinder is = 0.5*M*R^2
I = 0.5*M*R^2 + M*h^2
I = M*(0.5R^2 + h^2)
- From conservation of total mechanical energy of the cylinder, the change in gravitational potential energy ΔP.E plus the change in kinetic energy ΔK.E of the cylinder must be zero:
ΔP.E = ΔK.E
M*g*h = 0.5*I*w^2
M*g*h = 0.5*M*(0.5R^2 + h^2)*w^2
w^2 = 2*g*h / (0.5R^2 + h^2)
w = sqrt [2*g*h / (0.5R^2 + h^2)]
Where,
w: The angular speed of the cylinder
