A mass of 1kg is placed at 1m,2m,0.Another mere of 2kg is placed at 3m,4m,0.Find moment of inertia of both the ladder about z-axis
To calculate the moment of inertia of the ladders about the z-axis, we first need to find the distance of each ladder from the z-axis.
Given that the mass of the first ladder is 1kg and it is located at coordinates (1, 2, 0), the distance of the ladder from the z-axis is the x-coordinate, which is 1 meter.
Similarly, for the second ladder with a mass of 2kg at coordinates (3, 4, 0), the distance from the z-axis is again the x-coordinate, which is 3 meters.
The moment of inertia of each ladder can be calculated using the formula:
I = m * r^2
where I is the moment of inertia, m is the mass, and r is the distance from the axis of rotation.
For the first ladder:
I1 = 1kg * (1m)^2 = 1kg * 1m^2 = 1 kg*m^2
For the second ladder:
I2 = 2kg * (3m)^2 = 2kg * 9m^2 = 18 kg*m^2
Therefore, the moment of inertia of the first ladder about the z-axis is 1 kg*m^2, and the moment of inertia of the second ladder is 18 kg*m^2.