Let's choose east as positive x-direction and south as positive y-direction. We can resolve the two displacement along these two axes:
- Displacement 1 (3.5 km, south of west
- Displacement 2 (2.7 km, east of south
So, the total components on the two directions are
And the magnitude of the hiker's resultant displacement is
a) Object C (the disk) has the greatest rotational inertia ()
b) Object B (the sphere) has the smallest rotational inertia ()
Explanation:
The moments of inertia of the three objects are the following:
1) For a hoop of negligible thickness, it is
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
2) For a solid sphere, the moment of inertia is
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
3) For a disk of negligible thickness, the moment of inertia is
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
So now we can answer the two questions:
a) Object C (the disk) has the greatest rotational inertia ()
b) Object B (the sphere) has the smallest rotational inertia ()
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