Calculating Angular Velocity of a Shell Exiting a Barrel | Physics Homework

[paragchitnis]

Homework Statement

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 uniform acceleration, find the angular velocity of its axial rotation at the moment when the shell escapes the barrel.

Homework Equations

vf = vi + at
This equation can be used for linear as well as angular velocity
x = vit + at^2
vf^2 - vi^2 = 2ax

The Attempt at a Solution

The given answer is 2pi nv/l = 2.0 x 10³ rad./s

 

[housemartin]

How much time it took to make those n = 2 turns? then if you know this time, can you find angular velocity?

 

[paragchitnis]

How much time it took to make those n = 2 turns? then if you know this time, can you find angular velocity?

Time is not given. But let us consider it take ts for n = 2 turns. can we get the answer in terms of t?

 

[housemartin]

Time is what you have to find, you know final ant initial linear velocities and the length of the barrel, from here you can find ts. Angular velocity is measured in radians per second. And two rotations is how much radians? And you when you find time it took to make those two rotations, then...? ;]

 

[rwisz]

I would approach this problem by first understanding the physical principles involved. The given equation vf = vi + at suggests that the shell is undergoing constant acceleration while inside the barrel. This is further supported by the equation vf^2 - vi^2 = 2ax, which relates the final velocity to the initial velocity, acceleration, and displacement.

To calculate the angular velocity of the shell, we need to consider the rotational motion of the shell as it exits the barrel. The shell has made n = 2.0 turns inside the barrel, which means that it has rotated by an angle of 2pi radians. The length of the barrel, l = 2.0m, can be used to determine the circumference of the barrel, which is equal to 2pi x l = 4pi m.

We can then use the formula for angular velocity, ω = Δθ/Δt, where Δθ is the change in angle and Δt is the change in time. In this case, the change in angle is 2pi radians and the change in time is the time it takes for the shell to exit the barrel, which can be calculated using the given equation x = vit + at^2.

Plugging in the given values, we get x = 2.0m = (320m/s)t + (1/2)a(t^2). Solving for t, we get t = 0.0125s. Therefore, the angular velocity of the shell at the moment of exiting the barrel is ω = (2pi rad)/(0.0125s) = 2.0 x 103 rad/s, which is the same as the given answer.

In conclusion, the angular velocity of the shell exiting the barrel can be calculated by considering the rotational motion of the shell and using the given equations for linear motion. This approach is based on the fundamental principles of physics and provides a logical and systematic solution to the problem.