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} = m_{1}r_{1}^{2} +
m_{2}r_{2}^{2} +
m_{3}r_{3}^{2} +
m_{4}r_{4}^{2}

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= m_{1}x_{1}^{2} =
5.912(-2.5)^{2}= 36.95 kg-m^{2}

Moment of inertial of m2 about y axis

Iy2 = 5(2.9)^{2}= 42.05 kg-m^{2}

Iy3= Moment of inertial of m3 about y axis =
m_{3}x_{3}^{2.} =0

Iy4 = moment of inertia of m4 about y axis =
m_{4}x_{4}^{2} =0

Rotational kinetic energy of m1

= Iy1 × w^{2}/2 = 36.95 (4.19)^{2}/2= 324.35
J

Rotational energy of m2

= Iy2 × w^{2}/2 = 42.05 (4.19)^{2}/2=
369.12J

Rotaional energy of m3 = Iy3. × w^{2} / 2 = 0

Rotational energy of m4 = Iy4. × w^{2}/2 =0

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