May 10th, 2017, 01:39 AM  #1 
Member Joined: Jan 2016 From: Blackpool Posts: 40 Thanks: 0  Parametric equation
A metal bar has one end fixed at the origin, and rotates anticlockwise at a constant rate of ω radians per second; at time t = 0 it points along the xaxis. A beetle, starting at the origin, walks along the bar at a constant speed of v metres per second. What is its position at time t? I know that the position of the end of the bar at time t is (Rcos(wt), Rsin(wt)). But how do I get the position of the beetle? Thanks! Last edited by skipjack; May 10th, 2017 at 03:37 AM. 
May 10th, 2017, 03:38 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 17,919 Thanks: 1383 
At time t, how far along the bar has the beetle gone?

May 10th, 2017, 03:41 AM  #3 
Math Team Joined: Jul 2011 From: Texas Posts: 2,623 Thanks: 1303 
Beetle's distance from the origin is $r(t) = vt$ ... $x= vt \cdot \cos(\omega t)$ $y = vt \cdot \sin(\omega t)$ Beetle's path of travel for a single rotation of the bar will resemble the attached graph ... 

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