- #1

sergiokapone

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## Homework Statement

In opposite points carousel diameter D = 20 m, rotating with constant angular acceleration, located at the point C shooter and target M. Shooter aiming at a target without introducing amendments to the rotation of the carousel. What should be the angular acceleration of the carousel with that under these conditions, the bullet hit the target at the time the shot was carousel angular velocity ##\omega_0## = 1 rad / min, and the velocity ##v_0## = 200 m / s. Shoter and shooting conditions are assumed ideal. Neglect the influence of centrifugal force.

## Homework Equations

The equation of motion in non-inertial reference frame

##\frac{{d\vec v}}{{dt}} = - \left[ {\vec \beta \times \vec r} \right] + 2\left[ {\vec v \times \vec \omega } \right]##

## The Attempt at a Solution

Projected on the axis:

##\begin{array}{l}

\frac{{d{v_y}}}{{dt}} = 0\\

\frac{{d{v_x}}}{{dt}} = 2{v_y}\omega + \beta y

\end{array}##

and

##\omega = {\omega _0} + \beta t##

##y = {v_0}t - \frac{D}{2}## - from the first equation of motion

I finally got

##\frac{{d{v_x}}}{{dt}} = 2{v_0}\omega + 3{v_0}\beta t - \frac{{\beta D}}{2}##

integrating this equation, I get

##x=v_0 \omega_0 t^2+1/2v_0\beta t^{3}-1/4\beta D{t}^{2}##

From the ##y = {v_0}t - \frac{D}{2}## I find time, when the bullet hit the target (##y=D/2##)

##\tau=D/v_0##

when the bullet hit the target ##x=0##

solving ##0=v_0 \omega_0 t^2+1/2v_0\beta t^{3}-1/4\beta D{t}^{2}##

I find the angular acceleration. ##\beta=-\frac{4v_0\omega_0}{D}##

But it is negative!

Help me find the error!

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