The triceps muscle in the back of the upper arm is primarily used to extend the forearm. suppose this muscle in a professional boxer exerts a force of 1.75 × 103 n with an effective perpendicular lever arm of 3.05 cm, producing an angular acceleration of the forearm of 115 rad/s2. what is the moment of inertia of the forearm, in kilogram meters squared?

To solve this problem it is necessary to apply the concepts related to Torque as a function of the Force and the distance radius where it is applied.

By definition the Torque can be expressed as

Where

F = Force exerted

r = Radius

Substituting we have to

Through the second definition of the rotational Torque we can then find the moment of inertia for which we have to

Where

I = Moment of inertia

Angular acceleration

Replacing

Therefore the moment of inertia is

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.