Suppose you are riding a stationary exercise bicycle, and the electronic meter indicates that the wheel is rotating at 9.1 rad/s and that you have been riding for a "distance" of 8.6 x 103m. The wheel has a radius of 0.45 m. For how many minutes have you been riding your bike?
v=ωR
t=s/v= s/ ωR=8600/9.1•0.45=2100 s=35 min
To find out how many minutes you have been riding your bike, we can use the formula:
Time = Distance / Speed
First, let's convert the distance from meters to kilometers:
Distance = 8.6 x 10^3 m = 8.6 km
Now, let's calculate the time:
Time = Distance / Speed
= 8.6 km / 9.1 rad/s
Before we proceed, we need to convert the angular speed from rad/s to km/h.
1 rad/s = 1 * (2π/360) * r * h / (1000) km/h
2π/360 is the conversion factor to convert radians to degrees.
1000 is the conversion factor to convert meters to kilometers.
Angular Speed in km/h = 9.1 * (2π/360) * 0.45 * 60 km/h
Now, let's substitute the values:
Time = 8.6 km / (9.1 * (2π/360) * 0.45 * 60) hours
To convert the time to minutes, we multiply the result by 60:
Time (in minutes) = Time (in hours) * 60
Now, we can calculate the time in minutes.
To determine the time you have been riding your bike, we need to use the equation for angular velocity:
angular velocity (ω) = distance traveled (s) / time taken (t)
We can rearrange this equation to solve for time:
time taken (t) = distance traveled (s) / angular velocity (ω)
Given that the wheel is rotating at 9.1 rad/s and you have traveled a distance of 8.6 x 10^3 m, we can substitute these values into the equation:
time taken (t) = (8.6 x 10^3 m) / (9.1 rad/s)
Calculating this expression will give you the time taken in seconds. To convert it to minutes, divide the result by 60, as there are 60 seconds in a minute:
time taken (t) = (8.6 x 10^3 m) / (9.1 rad/s) / 60
By evaluating this expression, you will get the time you have been riding your bike in minutes.