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Black_prince [1.1K]
3 years ago
8

1. Consider three objects: Object A is a hoop of mass m and radius r; Object B is a sphere

Physics
1 answer:
Zarrin [17]3 years ago
7 0

a) Object C (the disk) has the greatest rotational inertia (\frac{3}{2}mr^2)

b) Object B (the sphere) has the smallest rotational inertia (\frac{4}{5}mr^2)

Explanation:

The moments of inertia of the three objects are the following:

1) For a hoop of negligible thickness, it is

I=MR^2

where M is its mass and R its radius. For the hoop in this problem,

M = m

R = r

Therefore, its moment of inertia is

I=(m)(r)^2=mr^2

2) For a solid sphere, the moment of inertia is

I=\frac{2}{5}MR^2

where M is its mass and R its radius. For the sphere in this problem,

M = 2m

R = r

Therefore, its moment of inertia is

I=\frac{2}{5}(2m)(r)^2=\frac{4}{5}mr^2

3) For a disk of negligible thickness, the moment of inertia is

I=\frac{1}{2}MR^2

where M is its mass and R its radius. For the disk in this problem,

M = 3m

R = r

Therefore, its moment of inertia is

I=\frac{1}{2}(3m)(r)^2=\frac{3}{2}mr^2

So now we can answer the two questions:

a) Object C (the disk) has the greatest rotational inertia (\frac{3}{2}mr^2)

b) Object B (the sphere) has the smallest rotational inertia (\frac{4}{5}mr^2)

Learn more about inertia:

brainly.com/question/2286502

brainly.com/question/691705

#LearnwithBrainly

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