A bicycle is rolling down a circular portion of a path; this portion of the path has a radius of 8.73 m. As the drawing illustrates, the angular displacement of the bicycle is θ = 0.979 rad. What is the angle (in radians) through which each bicycle wheel

(radius = 0.320 m)
rotates?
s=0.979*8.73=8.55m
angle in rad=8.55/0.320=26.71

This will help you get to the correct answer: This is what Wiley gave for the Tutorial hints

(a) Based on the drawing, what is the circular arc length traveled by the axle of the wheel?

The circular arc length traveled by the axle of the wheel is equal to the angular displacement θ, multiplied by the radius of the path minus the radius of the wheel.

From elementary geometry, the arc length is equal to the angle multiplied by the radius. The radius of the arc that the axle travels is equal to the radius of the path minus the wheel’s radius. Therefore, the arc length traveled by the axle is just the angular displacement multiplied by the radius of the path minus the radius of the wheel.

So essentially what you do is this:

1.) S = theta x (radius of path- radius of wheel) = the displacement travelled by the axle of the wheel

2.) Angle in radians: theta = S (displacement above) / radius of bike

Hope this helps!

Well, the bicycle wheel sure knows how to roll with the punches! In this case, the angular displacement of the bicycle is given by θ=0.979 rad. If we multiply that by the radius of the circular path, which is 8.73 m, we get the total distance covered by the bicycle, which is approximately 8.55 m.

Now here's where the wheels come into play! We can find the angle (in radians) through which each bicycle wheel rotates by dividing the distance covered by the bicycle (8.55 m) by the radius of the wheel (0.320 m). Grab your calculator and you'll find that the angle of rotation for each wheel is about 26.71 radians.

So remember, when it comes to biking, always keep an eye on the "wheelie" important details!

To find the angle (in radians) through which each bicycle wheel rotates, you can use the formula:

angle = distance / radius

In this case, the distance traveled by the bicycle is given as 8.55 m (calculated as 0.979 * 8.73), and the radius of each wheel is given as 0.320 m.

Plugging in these values into the formula, we get:

angle = 8.55 m / 0.320 m = 26.71 radians

Therefore, the angle through which each bicycle wheel rotates is approximately 26.71 radians.

To find the angle (in radians) through which each bicycle wheel rotates, we can use the formula:

angle in radians = distance traveled / radius of the wheel

First, we need to calculate the distance traveled by the bicycle using the angular displacement. The formula to find the distance traveled, s, is given by:

s = θ * r

where θ is the angular displacement and r is the radius of the circular path.

In this case, the angular displacement is given as θ = 0.979 rad and the radius of the circular path is 8.73 m. So, we can substitute the values into the formula:

s = 0.979 * 8.73 = 8.55 m

Now, we can calculate the angle (in radians) through which each bicycle wheel rotates using the formula mentioned earlier:

angle in radians = s / radius of the wheel

Here, the radius of each bicycle wheel is given as 0.320 m. Substituting the values into the formula:

angle in radians = 8.55 m / 0.320 m = 26.71 radians

Therefore, the angle through which each bicycle wheel rotates is 26.71 radians.

.979 * 8.73 = 8.55 meters along the path

.32 theta = 8.55
so
theta = 26.7 rad
yes