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.
Answer:
Explanation:
P = mgh/t = 20(9.8)(4) / 5 = 156.8 W(atts)
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The distance covered by car is equal to (assuming it is moving by uniform motion) the product between the car's speed and the time of the car ride, 4 h:
where
is the car's speed
is the duration of the car ride
Similarly, the distance covered by train is equal to the product between the train's speed and the duration of the train ride, 7 h:
The total distance covered is S=255 km, which is the sum of the distances covered by car and train:
which becomes
(1)
we also know that the train speed is 5 km/h greater than the car's speed:
(2)
If we put (2) into (1), we find
and if we solve it, we find
So, the car speed is 20 km/h and the train speed is 25 km/h.
