The radius of a motorcycle wheel is 35 cm. How many revolutions per minute must it make to keep a speed of 66 km/h?
500 rpm
Step 1: Convert the speed into SI units (m/s).
Given speed = 66 km/h
We know: \(1\,\text{km} = 1000\,\text{m}\) and \(1\,\text{h} = 3600\,\text{s}\).
So, \(66\,\text{km/h} = 66 \times \dfrac{1000}{3600}\,\text{m/s} = 18.33\,\text{m/s} \).
Step 2: Convert the radius into metres.
Radius = 35 cm = \(\dfrac{35}{100} = 0.35\,\text{m}\).
Step 3: Find the distance travelled in one revolution.
Distance in one revolution = circumference = \(2 \pi r\).
So, \(2 \pi (0.35) = 0.7 \pi \approx 2.2\,\text{m}\) (taking \(\pi = \tfrac{22}{7}\)).
Step 4: Find the number of revolutions per second.
Revolutions per second = \( \dfrac{\text{distance travelled in 1 second}}{\text{distance in 1 revolution}} \).
Distance in 1 second = speed = 18.33 m.
So, revolutions per second = \( \dfrac{18.33}{2.2} \approx 8.33 \).
Step 5: Convert revolutions per second to revolutions per minute.
1 minute = 60 seconds.
Revolutions per minute = \( 8.33 \times 60 = 500 \).
Final Answer: 500 revolutions per minute (rpm)