The moment of inertia (I) for a point mass is given by the equation I = m*r^2, where m is the mass and r is the distance from the axis of rotation. In this case, the axis of rotation is the z-axis.

For the 4.0-kg mass at (3.0, 4.0) m, the distance from the z-axis is the magnitude of the position vector, which is sqrt(3.0^2 + 4.0^2) = 5.0 m. So, the moment of inertia of the 4.0-kg mass is I1 = 4.0 kg * (5.0 m)^2 = 100 kg·m^2.

For the 7.0-kg mass at (3.0, -4.0) m, the distance from the z-axis is also 5.0 m. So, the moment of inertia of the 7.0-kg mass is I2 = 7.0 kg * (5.0 m)^2 = 175 kg·m^2.

The total moment of inertia of the system is the sum of the moments of inertia of the individual masses, which is I1 + I2 = 100 kg·m^2 + 175 kg·m^2 = 275 kg·m^2.

So, the answer is a. 275 kg·m^2.

Question

The moment of inertia (I) for a point mass is given by the equation I = m*r^2, where m is the mass and r is the distance from the axis of rotation. In this case, the axis of rotation is the z-axis.

For the 4.0-kg mass at (3.0, 4.0) m, the distance from the z-axis is the magnitude of the position vector, which is sqrt(3.0^2 + 4.0^2) = 5.0 m. So, the moment of inertia of the 4.0-kg mass is I1 = 4.0 kg * (5.0 m)^2 = 100 kg·m^2.

For the 7.0-kg mass at (3.0, -4.0) m, the distance from the z-axis is also 5.0 m. So, the moment of inertia of the 7.0-kg mass is I2 = 7.0 kg * (5.0 m)^2 = 175 kg·m^2.

The total moment of inertia of the system is the sum of the moments of inertia of the individual masses, which is I1 + I2 = 100 kg·m^2 + 175 kg·m^2 = 275 kg·m^2.

So, the answer is a. 275 kg·m^2.

Knowee AI · Accepted Answer

The moment of inertia (I) for a point mass is given by the equation I = m*r^2, where m is the mass and r is the distance from the axis of rotation. In this case, the axis of rotation is the z-axis.

For the 4.0-kg mass at (3.0, 4.0) m, the distance from the z-axis is the magnitude of the position vector, which is sqrt(3.0^2 + 4.0^2) = 5.0 m. So, the moment of inertia of the 4.0-kg mass is I1 = 4.0 kg * (5.0 m)^2 = 100 kg·m^2.

For the 7.0-kg mass at (3.0, -4.0) m, the distance from the z-axis is also 5.0 m. So, the moment of inertia of the 7.0-kg mass is I2 = 7.0 kg * (5.0 m)^2 = 175 kg·m^2.

The total moment of inertia of the system is the sum of the moments of inertia of the individual masses, which is I1 + I2 = 100 kg·m^2 + 175 kg·m^2 = 275 kg·m^2.

So, the answer is a. 275 kg·m^2.

A 4.0-kg mass is placed at (3.0, 4.0) m, and a 7.0 kg-mass is placed at (3.0, −4.0) m. What is the moment of inertia of this system of masses about the z axis?Select one:a.275 kg·m2b.250 kg·m2c.180 kg·m2d.90 kg·m2

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