A bike tire spins at a rate of 4 revolutions per second. If the diameter of the tire is 60cm?

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L

A bike tire spins at a rate of 4 revolutions per second. If the diameter of the tire is 60cm what is the average rate of change in height of a point on the tire for the first 1/100 second if h(0) = 30 for that point?

Answer
The general equation for height at time t is h(t) = r*sin(2*pi*f*t) + h_0. We use sin because height is the y-value of the point, r is the radius, h_0 is the initial height, and f is the frequency in revolutions per second.

So in your case, we have
r = 60cm
f = 4 rev/s
h_0 = 30cm

Our equation becomes

h(t) = 60*sin(8*pi*t) + 30

Now, compute h(1/100) = 60*sin(8*pi*1/100) + 30 = 60*sin(2*pi/25) + 30 = 44.92cm

So, the average rate of change is the change in height divided by the change in time. In other words, final minus initial height, divided by final minus initial time.

h(1/100) - h(0)
-------------------
1/100 - 0

=

(44.92 - 30) cm
---------------
1/100 s

= 1492 cm/s

Are there cyclometers for stationary bikes?

Ian F

With fall and winter coming on, I am finding myself indoors a lot more. My school has some very nice spinning bikes at the gym set off by themselves. However, they don't give any output (cadence, watts, mph, etc). I want to put in a good winter of training but I would like some readings to track my progress. I could get a stand alone heart monitor and try that but do they make cyclometers for stationaries?

Answer
get a heart rate monitor


that;s the bottom line anyway

how many hours did you do, and in what aerobic zones?

miles don;t mean anything
watts either really

a lot of stationary bikes have HRMs, it;s easy to sense heart beat through the hands, but they may not have a lot of statistical reporting

the most basic HRM just says what your heart rate is, right now, no history, no % of max, no nothing, just beats per minute



wle

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