Question

A shell acquires the initial velocity $v=320m/s$, having made $n=2.0$ turns inside the barrel whose length is equal to $l=2.0m$. Assuming that the shell moves inside the barrel with a uniform acceleration, the angular velocity in rad/s of its axial rotation at the moment when the shell escapes the barrel, to the nearest integer will be:

Answer 1

The shell acquires a constant angular acceleration at the same time as it accelerates linearly.
The two are related by (assuming both are constant)
$\frac{w}{l}=\frac{\beta }{2\pi n}$
Where $w=$ linear acceleration and $\beta =$angular acceleration
Then $\omega =\sqrt{2\beta 2\pi n}=\sqrt{2\frac{w}{l}(2\pi n{)}^2}$
But ${\nu }^2=2wl$, hence finally
$\omega =\frac{2\pi n\nu }{l}$