The angular velocity of a wheel moving at 5 km/h with a radius of 20.3cm is 65.33454149913602 rpm.

$$RPM = \frac{ 25 \times 5 }{3\times\pi\times 20.3} = 0.65334541499$$

You can check this result on this online converter

To find the revolutions per minute (RPM) of an object moving at a certain speed, you need to first determine how far it travels in one revolution, which is the circumference of the circle it forms. Then, use this information along with the speed to find the RPM.

Given:

• Radius (r) = 20.3 cm
• Speed = 5 km/h

Step 1: Find the circumference of the circle

The circumference $C$ of a circle is given by the formula:
$$C = 2 \pi r$$

Convert the radius from centimeters to kilometers to keep the units consistent:

• Radius = 20.3 cm = 0.000203 km

Now, calculate the circumference:
$$C = 2 \pi \times 0.000203$$
$$C \approx 0.00127548661 \text{km}$$

Step 2: Convert speed to km/min

Convert 5 km/h to kilometers per minute:
$$5 \text{ km/h} = \frac{5}{60} \text{ km/min}$$
$$\approx 0.0833 \text{ km/min}$$

Step 3: Find revolutions per minute (RPM)

To find the RPM, divide the speed in km/min by the circumference in km:
$$\text{RPM} = \frac{0.0833 \text{ km/min}}{0.00127548661 \text{ km}}$$

$$\text{RPM} \approx 65.33$$

Therefore, the RPM is approximately $65.33$.