A bicycle with 55.20 cm diameter wheels is traveling at 23.60 km/hr.

At what angular speed do the wheels turn?

How long do they take to turn once around?

change km/hr to m/s.

tangentialspeed=w*r
w=tangential speed in m/s / radius in m.

23.34 Rad/Sec

To find the angular speed of the wheels, we need to convert the linear speed of the bicycle into angular speed.

The linear speed of the bicycle can be converted from km/hr to cm/s:
23.60 km/hr * (100000 cm/1 km) * (1 hr/3600 s) = 655.56 cm/s

The circumference of a wheel can be found using the formula:
C = π * diameter

In this case, the diameter of the wheel is 55.20 cm. So, the circumference of the wheel is:
C = π * 55.20 cm = 173.76 cm

Since the linear speed of the wheel is equal to the circumference times the angular speed, we can solve for the angular speed:
Linear speed = Circumference * Angular speed

655.56 cm/s = 173.76 cm * Angular speed

Now, let's solve for the angular speed:
Angular speed = 655.56 cm/s / 173.76 cm
Angular speed ≈ 3.77 radians/s

Therefore, the angular speed of the wheels is approximately 3.77 radians/s.

To find how long it takes for the wheels to turn once around, we can use the formula:
Time = (2π) / Angular speed

Time = (2 * π) / 3.77 radians/s
Time ≈ 1.67 seconds

Therefore, the wheels take approximately 1.67 seconds to turn once around.

To find the angular speed of the wheels, we need to convert the linear speed of the bicycle to angular speed.

1. First, let's convert the speed from km/hr to cm/s:
- We know that 1 km = 100,000 cm and 1 hr = 60 min = 60 s.
- Therefore, the speed of the bicycle is 23.60 km/hr = 23.60 * 100,000 cm / (60 * 60) s = 65.556 cm/s.

2. Now, let's find the circumference of the wheel:
- The circumference of a circle is given by the formula C = π * d, where d is the diameter.
- The diameter of the wheel is 55.20 cm, so the circumference is C = π * 55.20 cm ≈ 173.561 cm.

3. The linear speed of the bicycle is equal to the product of the angular speed of the wheels and the radius of the wheels.
- Linear speed = Angular speed * Radius
- Since the radius is half the diameter, the radius of the wheel is 55.20 cm / 2 = 27.60 cm.
- We can rearrange the equation to find the angular speed:
Angular speed = Linear speed / Radius = 65.556 cm/s / 27.60 cm ≈ 2.3756 rad/s.

Therefore, the angular speed at which the wheels turn is approximately 2.3756 rad/s.

To find the time taken for the wheels to turn once around, we need to calculate the period of rotation.

4. The period of rotation is defined as the time taken for one complete revolution:
- The period (T) is equal to 2π divided by the angular speed (ω).
- T = 2π / ω = 2π / 2.3756 rad/s ≈ 2.6478 s.

Therefore, the wheels take approximately 2.6478 seconds to complete one full revolution.