Question

4.) A unknown point mass is located at x = -2.5 m, y = 0 m, a point mass of 5 kg is located at x = +2.9 m, y = 0 m, a point mass of 2 kg is located at x = 0 m, y = -2 m, and a point mass of 2 kg is located at x = 0 m, y = +2 m. The moment of inertia about the z axis (origin) is 95 kg m2. If the masses are the same and locations do not change, what is their rotational kinetic energy if they are spinning about the y axis at 4.19 rad/s, in Joules?

Answer 1

let unknown mass is m

Moment of inertial of four mass system about z axis through origin is

I_z = m₁r₁² + m₂r₂² + m₃r₃² + m₄r₄²

95= m(-2.5)² + 5(2.9)²+2×(-2)²+2(2)²

95=6.25 m + 58.05

m= 5.912 kg

I_y = moment of inertia about y axis

Iy1= m₁x₁² = 5.912(-2.5)²= 36.95 kg-m²

Moment of inertial of m2 about y axis

Iy2 = 5(2.9)²= 42.05 kg-m²

Iy3= Moment of inertial of m3 about y axis = m₃x₃^2. =0

Iy4 = moment of inertia of m4 about y axis = m₄x₄² =0

Rotational kinetic energy of m1

= Iy1 × w²/2 = 36.95 (4.19)²/2= 324.35 J

Rotational energy of m2

= Iy2 × w²/2 = 42.05 (4.19)²/2= 369.12J

Rotaional energy of m3 = Iy3. × w² / 2 = 0

Rotational energy of m4 = Iy4. × w²/2 =0