You are in charge of developing a new weapon that can be used to project circula

Question

You are in charge of developing a new weapon that can be used to project circular projectiles at high speed. The idea is to place them inside of a frictionless tube that rotates in the horizontal x-y plane with a constant angular velocity do omega about the z-axis. A projectile of mass m is injected into the tube at a radial distance L_0 with release speed v_0. The tube end is at distance L_1. Derive the differential equation describing the projectile's displacement r as a function of time. Solve a) to find the equation for radial position r(t) of the projectile under the given initial conditions using variables only (no numbers). Find the equation for radial velocity v(t) using variables only.

Explanation / Answer

a) differential equation describing projectile displacement

dr(t)/dt = w * d2x/dt2 + Lo * t

b) radial position r(t)

=>   r(t) =   Lo + (L1 * w)t + 1/2gt2

c) radial velocity v(t)

=> v(t) = w * Lo + gt

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