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Answer:
a) 230 Km b) 76.7 km/h c) Please see below
Explanation:
a) If we can neglect the time while the driver accelerated, the movement can be divided in two parts, each of them at a constant speed:
⇒
b) The average x component of velocity, can be calculated applying the definition of average velocity, as follows:
If we choose t₀ = 0 and x₀ = 0, replacing xf and t by the values we have already found, we can find vavg,x as follows:
c) The found value of avg,x is not the same as the arithmetic average of the initial and final values of vx (70 Km/h) due to the time traveled at both velocities was not the same.
If the driver had droven half of the time (1.5 h) at 50 km/h and the other half at 90 km/h, total displacement would have been as follows:
Applying the definition of average velocity once more:
which is the same as the arithmetic average of the initial and final values of vₓ.
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.