Classical Mechanics (Kibble & Berkshire) · Problem 6.17

Orbits in a central field — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · constrained-motion-helix

Problem

A smooth wire has the form of the helix

x = a\cos\theta

y = a\sin\theta

z = b\theta

, where

\theta

is a real parameter, and

a

b

are positive constants. The wire is fixed with the axis

Oz

pointing vertically upwards. A particle

P

, which can slide freely on the wire, is released from rest at the point

(a, 0, 2\pi b)

. Find the speed of

P

when it reaches the point

(a, 0, 0)

and the time taken for it to do so.