Question

A 133-kg horizontal platform is a uniform disk of radius 1.51 m and can rotate about the vertical axis through its center. A 66.5-kg person stands on the platform at a distance of 1.07 m from the center and a 27.5-kg dog sits on the platform near the person, 1.39 m from the center. Find the moment of inertia of this system, consisting of the platform and its population, with respect to the axis. _____ kg*m^2

Answer 1

Moment of interia of a uniform disc about the vertical axis of rotation = (1/2) * M* R²

M = mass of disk = 133 Kg,            R = Radius of disk = 1.51 m

Moment of interia due to n- particals= m₁ r₁² + m₂ r₂² + -----------------------+ m_n r_n²

m1, m2, ----------------m _n are the masses of 1st , 2nd, -------- nth particle.

r1, r2,   ---------------------r_n are the distances of the particles from the axis of rotation.

Moment of interia of the plateform and population :

I = ( 1/2) M* R² + m_p*r_p² + m_d *r_d²                                   -----------------------1

m_p = mass of person= 66.5 kg,            m_d = mass of dog= 27.5 kg

r_p = distance of man from center of disk = 1.07 m

r_d = distance of dof from the center of disk= 1.39 m

By putting all the values in eq. 1

I = 280.89 kg- m²