A55.0-kg woman stands at the rim of a horizontal turntable having a moment of inertia of 540 kg · m2 and a radius of 2.00 m. the turntable is initially at rest and is free to rotate about a frictionless vertical axle through its center. the woman then starts walking around the rim clockwise (as viewed from above the system) at a constant speed of 1.50 m/s relative to the earth.
(a) in what direction does the turntable rotate? counterclockwise or clockwise
with what angular speed does the turntable rotate? ? rad/s
(b) how much work does the woman do to set herself and the turntable into motion? ? j

a) ω = 0.305 rad/s counterclockwise

b) W = 61.875J

Explanation:

The angular speed of the woman is:

By conservation of the angular momentum:

 where ωo = 0

Solving for :

Work done by the woman is given by the variation on her kinetic energy:

coil wire, increase current, put iron inside the coil

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.