Four point masses are arranged on the xy plane as follows.
Mass1 = 47.0 grams at x = 2.00 cm and y = 2.00 cm.
Mass2 = 55.0 grams at x = 0.00 cm and y = 4.00 cm.
Mass3 = 27.0 grams at x = -3.00 cm and y = -3.00 cm.
Mass4 = 45.0 grams at x = -1.00 cm and y = 2.00 cm.
What is the rotational inertia if this collection of masses is rotating about the x axis?
wouldn't it be the sum of the masses at their y locations...
Itotal= 1/2 m1(y1)^2+ 1/2 m2(y2)^2+ ..
thank you very much!, really appreciate it!
To find the rotational inertia of the collection of masses rotating about the x-axis, we need to calculate the moment of inertia for each mass and then sum them up.
The moment of inertia for a point mass rotating about an axis is given by the formula:
I = m * r^2
where I is the moment of inertia, m is the mass of the point, and r is the perpendicular distance between the point mass and the axis of rotation.
For each point mass in the collection:
Mass1:
m1 = 47.0 grams = 0.047 kg
r1 = distance from the x-axis = 2.00 cm = 0.02 m
(moment of inertia for Mass1) I1 = m1 * r1^2
Mass2:
m2 = 55.0 grams = 0.055 kg
r2 = distance from the x-axis = 4.00 cm = 0.04 m
(moment of inertia for Mass2) I2 = m2 * r2^2
Mass3:
m3 = 27.0 grams = 0.027 kg
r3 = distance from the x-axis = 3.00 cm = 0.03 m
(moment of inertia for Mass3) I3 = m3 * r3^2
Mass4:
m4 = 45.0 grams = 0.045 kg
r4 = distance from the x-axis = 2.00 cm = 0.02 m
(moment of inertia for Mass4) I4 = m4 * r4^2
Now, sum up the individual moments of inertia to get the total rotational inertia of the system about the x-axis:
Total moment of inertia (I_total) = I1 + I2 + I3 + I4
You can substitute the values of masses and distances into the formulas to get the numerical values for the individual moments of inertia, and then add them up to get the total rotational inertia.