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June 7th, 2014, 05:52 AM  #1 
Newbie Joined: Jun 2014 From: Princeton wv Posts: 4 Thanks: 0  Differential Speed
This may need to be in a different forum.... and may lead to a wager So we're in a poker game, and a guy poses a problem: A car is going 60 mph in a straight line, point A to point B. The car has 16" tires. Imagine a white dot painted on the outside of one of the tires. How fast is the spot going? Clearly, in one plane, the spot is going 60 mph (it will arrive at point B at exactly the same time as a similar spot painted directly above it on the fender). But the spot on the tire is also travelling up and down so it must in some sense be going faster than the car. Do we first need to define speed/fast? Then there was the question about the speed of the track on a moving tank, but we'll try that one later. It's a helluva poker game (I'm more the group philosopher than mathematician). Thanks 
June 7th, 2014, 03:52 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,950 Thanks: 1141 Math Focus: Elementary mathematics and beyond 
76.4 mph.
Last edited by greg1313; June 7th, 2014 at 04:35 PM. 
June 7th, 2014, 04:37 PM  #3 
Member Joined: Feb 2012 From: Hastings, England Posts: 83 Thanks: 14 Math Focus: Problem Solving  Hey, I know it's not my question but I like to read everyone's answers so would be nice to know how you actually have that answer with a brief explanation. oops changed your answer. I still think that the car can only travel as fast as the wheel is going, which happens to be at 60.m.p.h, the dot is not going up and down but round and round which is actually just the dot going forward isn't it? this is why explanations a re good simpletons like me Last edited by nmenumber1; June 7th, 2014 at 04:40 PM. 
June 7th, 2014, 04:50 PM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,950 Thanks: 1141 Math Focus: Elementary mathematics and beyond 
See this page. The arc length of the cycloid is 8 times the radius and the car travels 16 * pi inches per tire revolution so the ratio between the two speeds is about 1.2732. 1.2732 * 60 ≈ 76.4. 
June 7th, 2014, 05:06 PM  #5 
Member Joined: Feb 2012 From: Hastings, England Posts: 83 Thanks: 14 Math Focus: Problem Solving 
wow that's awesome thanks very much 
June 7th, 2014, 05:16 PM  #6 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,671 Thanks: 2651 Math Focus: Mainly analysis and algebra 
The spot doesn't travel at a constant speed. Indeed, when it's at the bottom of the tyre, it is stationary (unless the brakes are locked up or the wheels are spinning).

June 7th, 2014, 05:23 PM  #7 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,950 Thanks: 1141 Math Focus: Elementary mathematics and beyond 
I'm not sure I agree with that. The tyre is in constant motion. 
June 7th, 2014, 06:11 PM  #8 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,950 Thanks: 1141 Math Focus: Elementary mathematics and beyond 
Had to think about that!

June 7th, 2014, 06:41 PM  #9 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,671 Thanks: 2651 Math Focus: Mainly analysis and algebra  
June 8th, 2014, 01:10 PM  #10 
Senior Member Joined: Apr 2014 From: UK Posts: 939 Thanks: 335 
When the spot is at the top , it's going 120mph, vroom! (relative to the road) When the spot is at it's most forward or most rear it is matching the speed of 60mph. Tank tracks aren't really any different. 

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