The moment of inertia of the system can be calculated by summing the individual moments of inertia of each person around the axis of rotation.
The moment of inertia of a point mass rotating around an axis at a distance r is given by:
I = mr^2
where I is the moment of inertia, m is the mass of the object, and r is the distance from the axis of rotation.
For the first teenager weighing 60.0 kg, the moment of inertia around the axis of rotation can be calculated as:
I1 = m1r1^2 = 60.0 kg x (12.0 m)^2 = 8,640 kg m^2
For the second teenager weighing 45.0 kg, the moment of inertia around the axis of rotation can be calculated as:
I2 = m2r2^2 = 45.0 kg x (12.0 m)^2 = 6,480 kg m^2
For the third teenager weighing 80.0 kg, the moment of inertia around the axis of rotation can be calculated as:
I3 = m3r3^2 = 80.0 kg x (12.0 m)^2 = 11,520 kg m^2
The total moment of inertia of the system can be found by summing the individual moments of inertia:
Itotal = I1 + I2 + I3 = 8,640 kg m^2 + 6,480 kg m^2 + 11,520 kg m^2 = 26,640 kg m^2
Therefore, the moment of inertia for three teenagers weighing 60.0 kg, 45.0 kg, and 80.0 kg sitting at different points on the edge of a rotating stage, which has a radius of 12.0 m, is 26,640 kg m^2.
Determine the moment of inertia for three teenagers weighing 60.0 kg, 45.0 kg, and 80.0 kg sitting at different points on the edge of a rotating stage, which has a radius of 12.0 m.
1 answer