A majorette takes two batons and fastens them together in the middle at right angles to make an "x" shape. Each baton was 0.90 m long and each ball on the end is 0.20 kg. (Ignore the mass of the rods.) What is the moment of inertia if the arrangement is spun around an axis formed by one of the batons?Select one:a.0.064 kg·m2b.0.32 kg·m2c.0.081 kg·m2d.0.19 kg·m2
Question
A majorette takes two batons and fastens them together in the middle at right angles to make an "x" shape. Each baton was 0.90 m long and each ball on the end is 0.20 kg. (Ignore the mass of the rods.) What is the moment of inertia if the arrangement is spun around an axis formed by one of the batons?Select one:a.0.064 kg·m2b.0.32 kg·m2c.0.081 kg·m2d.0.19 kg·m2
Solution
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, we have two balls on the ends of the baton that is the axis of rotation, and two balls on the ends of the other baton.
For the balls on the ends of the axis of rotation, r = 0, so they do not contribute to the moment of inertia.
For the balls on the ends of the other baton, r = 0.45 m (half the length of the baton), and m = 0.20 kg.
So, the moment of inertia is I = 2*(mr^2) = 2(0.20 kg * (0.45 m)^2) = 0.081 kg·m^2.
So, the correct answer is c. 0.081 kg·m^2.
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