MHB Find angle in radians of tractor wheel going 22 mph in 12 s

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To find the angle in radians for a tractor wheel moving at 22 mph over 12 seconds, the discussion emphasizes using angular equations instead of linear ones. The formula v = rω is highlighted, where ω (angular velocity) is calculated by converting the linear speed to radians per second. The angle θ is then determined using the equation θ = ωt. The importance of unit conversions is also noted to ensure accuracy in calculations. This approach provides a systematic method for solving the problem.
karush
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View attachment 1469

the calculation is mine however, if ans is correct not sure what the conventional way would to set this up?
 
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karush said:
View attachment 1469

the calculation is mine however, if ans is correct not sure what the conventional way would to set this up?
I typically would include the actual formulas you are using. I also tend to use the angular equations rather than trying to use the linear ones. For example: [math]v = r \omega[/math], so [math]\omega = \frac{v}{r}[/math] (And at this step you would do your unit conversions.)

Then you simply have [math]\theta = \omega t[/math].

-Dan
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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