本题目来源于试卷: 2007美国US F=MA物理竞赛，类别为 美国F=MA物理竞赛
[单选题]
A uniform disk, a thin hoop, and a uniform sphere, jl)- yqjap1-g all with the same mass a 1-vu1 itka- 7x par3ihnd same outer radius, are each free to rotate about a fixed axis through its center. Assume the hoop is connected to the rotation axis by light spokes. With the objects starting from rest, identical forces are v 1 kh-u3iirt-a17xp a simultaneously applied to the rims, as shown. Rank the objects according to their kinetic energies after a given time $t$, from least to greatest. 
A. disk, hoop, sphere
B. sphere, disk, hoop
C. hoop, sphere, disk
D. disk, sphere, hoop
E. hoop, disk, sphere
参考答案: E
本题详细解析:
All objects experiencen xw90c o qw toper:(b2qs3x)* the same force $F$ at the same radius $R$, so the torque $\tau = FR$ is identical for all three.
Angular acceleration $\alpha = \tau / I$.
Angular velocity after time $t$ is $\omega = \alpha t = (\tau t) / I$.
Rotational kinetic energy $K = \frac{1}{2}I\omega^2 = \frac{1}{2}I \left( \frac{\tau t}{I} \right)^2 = \frac{(\tau t)^2}{2I}$.
Since $\tau$ and $t$ are identical, the kinetic energy $K$ is inversely proportional to the rotational inertia $I$ ($K \propto 1/I$).
The rotational inertias are: $I_{hoop} = mR^2$, $I_{disk} = \frac{1}{2}mR^2$, $I_{sphere} = \frac{2}{5}mR^2$.
Ordering the inertias from greatest to least: $I_{hoop} > I_{disk} > I_{sphere}$ (since $1 > 1/2 > 2/5$).
Therefore, the kinetic energies from least to greatest are in the opposite order: $K_{hoop} < K_{disk} < K_{sphere}$.
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