A person stands on a platform, initially at rest, that can rotate freely without friction. The moment of inertia of the person plus the platform is IP. The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia IW and angular velocity ωW. Take the ωW direction counterclockwise when viewed from above. Part A

What will be the angular velocity ωP of the platform if the person moves the axis of the wheel so that it points vertically upward?Part B

What will be the angular velocity ωP of the platform if the person moves the axis of the wheel so that it points at a 60 ∘ angle to the vertical?Part C

What will be the angular velocity ωP of the platform if the person moves the axis of the wheel so that it points vertically downward?Part D

What will ωP be if the person reaches up and stops the wheel in part A?

answer is given below

Explanation:

first we use here conservation of angular momentum in the vertical direction that is express as

angular velocity platform =  clock-wise     ..........................1

so the net angular momentum = 0

and

here when vertical angular momentum will be 0   than

here  angular velocity of the platform will be

ωP =  clock-wise       ..........................2

and

the angular velocity of the platform

ωP =    anti-clock-wise        ............................3

and

when here Platform will stop than

ωP = 0      ............................4

so as that conserve the angular momentum

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.