<span>The moment of inertia of the large sphere will be twice that of the smaller sphere.
The formula for the moment of inertia for a solid sphere is:
I = (2/5)mr^2
where
I = moment of inertia
m = mass
r = radius
Since both spheres have the same diameter, they also have the same radius, so the only change is their mass. And the moment of inertia is directly proportional to their mass as shown by the above formula. So the sphere with twice the mass will have twice the moment of inertia, or 2 times.</span>
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Angular frequency in radian per second for 20 vibrations in 10 seconds is 12.6 rad/s
<h3>What is Angular frequency?</h3>
Angular frequency is the number of vibrations in radian per second.
The total number of vibrations n is 20 and the time taken for these vibrations is 10 s
The frequency of the vibrations will be
f = 20 / 10 = 2 Hz
Angular frequency is related to the frequency as
ω = 2πf
ω=2π × 2
ω = 12.6 rad/s
Thus, the angular frequency is 12.6 rad/s.
Learn more about Angular frequency.
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