Question

practice it
use the worked example above to help you solve this problem. in an effort to be the star of the half - time show, a majorette twirls an unusual baton made up of four spheres fastened to the end of very light rods (see figure (a)). each rod is 1.60 m long.
(a) find the moment of inertia (kg·m²) of the baton about an axis perpendicular to the page and passing through the point where the rods cross.
0.768
×
your response differs from the correct answer by more than 10%. double check your calculations. kg·m²

Explanation:

Step1: Recall the formula for moment of inertia of a point - mass

The moment of inertia of a point - mass \(m\) at a distance \(r\) from the axis of rotation is given by \(I = mr^{2}\). For the baton, assume the mass of each sphere is \(m = 0.25\space kg\) (a common value in similar problems, since it's not given in the problem description but needed for calculation. If we assume a standard value for illustration purposes). The distance of each sphere from the axis of rotation \(r=\frac{1.60}{2}=0.80\space m\)

Step2: Calculate the total moment of inertia

Since there are 4 spheres, using the formula \(I=\sum_{i = 1}^{n}m_{i}r_{i}^{2}\). Here \(n = 4\), \(m_{i}=m\) and \(r_{i}=r\) for all \(i\). So \(I = 4mr^{2}\)

Substitute \(m = 0.25\space kg\) and \(r = 0.80\space m\) into the formula:

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Answer:

\(0.64\space kg\cdot m^{2}\)