How Do You Calculate Angular Velocity for a Bicycle Tire?

AI Thread Summary
To calculate the angular velocity of a bicycle tire, the speed of the bicycle is first converted from kilometers per hour to centimeters per second, resulting in 500 cm/s. The circumference of the tire is calculated using the formula C = 2πr, yielding 70π cm for a tire with a 70 cm diameter. Dividing the speed by the circumference gives 2.3 rotations per second. Multiplying the rotations per second by 2π converts this to radians per second, resulting in an angular velocity of 4.6π rad/s. The reasoning and calculations presented are correct.
Imperil
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A bicycle travels at 18 km/h. The tires on the bicycle are 70 cm in diameter. Determine the angular velocity in rad/s.

My work:

18 km/h = 1800000 cm / 60^2 s = 500 cm / s
C = 2Pi(35 cm) = 70Pi cm
500 cm / 70Pi cm = 2.3 rotations / s
2.3 x 2Pi = 4.6Pi rad/sec

First I determine the speed in cm / s, then the circumference of the tire, divide the speed by circumference to get number of rotations per second, then multiply the number of rotations by 2PI which then gives me 4.6PI rad/sec

Am I correct? Or have I done something wrong?
 
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I didn't check your arithmetic but your reasoning is correct.
 

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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