Answer:
Explanation:
During the swing , the center of mass will go down due to which disc will lose potential energy which will be converted into rotational kinetic energy
mgh = 1/2 I ω² where m is mass of the disc , h is height by which c.m goes down which will be equal to radius of disc , I is moment of inertia of disc about the nail at rim , ω is angular velocity .
mgr = 1/2 x ( 1/2 m r²+ mr²) x ω²
gr = 1/2 x 1/2 r² x ω² + 1/2r² x ω²
g = 1 / 4 x ω² r + 1 / 2 x ω² r
g = 3 x ω² r/ 4
ω² = 4g /3 r
= 4 x 9.8 / 3 x .25
= 52.26
ω = 7.23 rad / s .
There's only one question there.
The answer is "Greater amplitude".
Answer:
The angular velocity is
Explanation:
From the question we are told that
The mass of each astronauts is
The initial distance between the two astronauts
Generally the radius is mathematically represented as
The initial angular velocity is
The distance between the two astronauts after the rope is pulled is
Generally the radius is mathematically represented as
Generally from the law of angular momentum conservation we have that
Here is the initial moment of inertia of the first astronauts which is equal to the initial moment of inertia of the second astronauts So
Also is the initial angular velocity of the first astronauts which is equal to the initial angular velocity of the second astronauts So
Here is the final moment of inertia of the first astronauts which is equal to the final moment of inertia of the second astronauts So
Also is the final angular velocity of the first astronauts which is equal to the final angular velocity of the second astronauts So
So
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