Classical Mechanics (Kibble & Berkshire) · Problem 2.6

Newton's laws of motion and the law of gravitation — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · polar-coordinates-motion

Problem

An insect flies on a spiral trajectory such that its polar coordinates at time

t

are given by

r = be^{\Omega t}, \qquad \theta = \Omega t,

where

b

and

\Omega

are positive constants. Find the velocity and acceleration vectors of the insect at time

t

, and show that the angle between these vectors is always

\pi/4