The rotational kinetic energy of a rigid body with moment of inertia $I$ rotating at angular speed $\omega$ is:
$\frac{1}{2}I\omega^{2}$
$I\omega$
$\frac{1}{2}I\omega$
$I\omega^{2}$
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WhyRotational kinetic energy is $E_{k,rot}=\frac{1}{2}I\omega^{2}$, the rotational analogue of $\frac{1}{2}mv^{2}$.
3Multiple choice · Hard
A skater pulls in her arms while spinning, reducing her moment of inertia. With no external torque, her angular speed:
Increases
Decreases
Stays the same
Becomes zero
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WhyAngular momentum $L=I\omega$ is conserved. Reducing $I$ increases $\omega$, so she spins faster.
4Fill in the blank · Medium
The rotational analogue of mass, which measures resistance to angular acceleration, is the moment of .
Answer:
inertia
WhyMoment of inertia $I$ plays the role of mass in rotational dynamics, appearing in $\tau=I\alpha$.
5Multiple choice · Hard
A uniform disk of moment of inertia I = (1/2) M R squared is driven by a tangential force F at its rim. Its angular acceleration is
2F / (M R)
F / (M R)
F R / (2 M)
F / (2 M R)
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Whyalpha = torque / I = F R / ((1/2) M R squared) = 2F / (M R).
6Multiple choice · Medium
The rotational form of Newton's second law states that the angular acceleration of a rigid body equals
net torque divided by moment of inertia
moment of inertia divided by net torque
net torque times moment of inertia
net force divided by moment of inertia
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WhyAngular acceleration = net torque / moment of inertia.
7Fill in the blank · Medium
The torque produced by a force F acting tangentially at the rim of a wheel of radius R is F times .
Answer:
R / the radius / radius
WhyTorque = F R for a tangential force at radius R.
8Fill in the blank · Medium
The moment of inertia of a uniform solid disk of mass M and radius R about its central axis is M R squared.
Answer:
1/2 / 0.5 / one half
WhyI = (1/2) M R squared for a solid disk.
9Multiple choice · Hard
Equal angular impulses are delivered to a solid disk and a hoop of the same mass and radius. The body with the greater final rotational kinetic energy is
the disk, because it has the smaller moment of inertia
the hoop, because it has the smaller moment of inertia
the hoop, because it has the greater moment of inertia
neither; they have equal kinetic energy
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WhyEqual angular impulse gives equal L; K = L squared / (2 I), so the body with smaller I (the disk) has greater K.
10Multiple choice · Medium
The angular impulse delivered to a rotating body equals its change in
angular momentum
moment of inertia
rotational kinetic energy
angular position
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WhyAngular impulse (torque times time) equals the change in angular momentum.
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