Suppose you are riding a stationary exercise bicycle, and the electronic meter indicates that the wheel is rotating at 14.6 rad/s. The wheel has a radius of 0.435 m. If you ride the bike for 44.4 min, how far would you have gone if the bike could move?
To find the distance you would have gone if the bike could move, we need to calculate the circumference of the wheel and multiply it by the number of revolutions.
The circumference of the wheel is given by:
C = 2πr
where r is the radius of the wheel.
Plugging in the values, we have:
C = 2π(0.435)
C ≈ 2.73 m
Now we need to calculate the number of revolutions the wheel makes in 44.4 minutes. Since the wheel is rotating at a constant speed of 14.6 rad/s, we can multiply the angular velocity by the time to get the number of revolutions.
Number of revolutions = (angular velocity) x (time in seconds)
First, we need to convert 44.4 minutes to seconds:
44.4 min * 60 s/min = 2664 s
Number of revolutions = 14.6 rad/s * 2664 s ≈ 38850.24 rev
Finally, we can calculate the distance traveled by multiplying the circumference by the number of revolutions:
Distance traveled = Circumference * Number of revolutions
Distance traveled ≈ 2.73 m/rev * 38850.24 rev ≈ 106,052 m
Therefore, if the bike could move, you would have covered approximately 106,052 meters (or 106.052 kilometers) in 44.4 minutes.