A wheel is turning about an axis through its center with constant angular acceleration. Starting from rest, at t=0t=0, the wheel
1 answer:
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The angular velocity depends on the length of the orbit and the orbital
speed of the telescope.
Response:
First question:
- The angular velocity of the telescope is approximately <u>0.199 rad/s</u>
Second question:
- The telescope should accelerates away by approximately F = <u>0.0005·m </u>
Third question:
- <u>The pulling force between the Earth and the satellite</u>
The distance of the James Webb telescope from the Sun = 1.5 million kilometers from Earth on the side facing away from the Sun
The orbital velocity of the telescope = The Earth's orbital velocity
First question:
The orbital velocity of the Earth = 29.8 km/s
The distance between the Earth and the Sun = 148.27 million km
The radius of the orbit of the telescope = 148.27 + 1.5 = 149.77
Radius of the orbit, r = 149.77 million kilometer from the Sun
The length of the orbit of the James Webb telescope = 2 × π × r
Which gives;
r = 2 × π × 149.77 million kilometers ≈ 941.03 million kilometers
Therefore;
- The angular velocity of the telescope, ω ≈ <u>0.199 rad/s</u>
Second question:
Centrifugal force force, = m·ω²·r
Which gives;
Universal gravitational constant, G = 6.67408 × 10⁻¹¹ m³·kg⁻¹·s⁻²
Mass of the Sun = 1.989 × 10³⁰ kg
Which gives;
Which gives;
<
, therefore, the James Webb telescope has to accelerate away from the Sun
F = -
The amount by which the telescope accelerates away is approximately 0.00592·m - 0.0054233·m ≈ <u>0.0005·m (away from the Sun)</u>
Third part:
Other forces include;
- <u>The force of attraction between the Earth and the telescope </u>which can contribute to the the telescope having a stable orbit at the given speed.
Learn more about orbital motion here:
Answer:
the moment of inertia with the arms extended is Io and when the arms are lowered the moment
I₀/I > 1 ⇒ w > w₀
Explanation:
The angular momentum is conserved if the external torques in the system are zero, this is achieved because the friction with the ice is very small,
L₀ = L_f
I₀ w₀ = I w
w = w₀
where we see that the angular velocity changes according to the relation of the angular moments, if we approximate the body as a cylinder with two point charges, weight of the arms
I₀ = I_cylinder + 2 m r²
where r is the distance from the center of mass of the arms to the axis of rotation, the moment of inertia of the cylinder does not change, therefore changing the distance of the arms changes the moment of inertia.
If we say that the moment of inertia with the arms extended is Io and when the arms are lowered the moment will be
I <I₀
I₀/I > 1 ⇒ w > w₀
therefore the angular velocity (rotations) must increase
in this way the skater can adjust his spin speed to the musician.