Rotations per Minute . How many rotations per minute must a wheel of diameter 1.5 m make to

achieve a speed of 45 kmph ? (Approx pi= 3 ).

45km/hr * 1hr/60min * 1rev/(1.5π m) * 1000m/km = 159rev/min

To find the rotations per minute (RPM) of a wheel, we need to understand the relationship between the speed of the wheel and its RPM. The formula to related these two is:

RPM = (Speed / Circumference) * 60

First, let's find the circumference of the wheel. The formula for the circumference of a circle is C = π * d, where C is the circumference, π is approximately 3, and d is the diameter.

C = π * d
C = 3 * 1.5
C = 4.5 m

Now, let's convert the given speed from km/h to m/s. There are 1000 meters in 1 kilometer, and 1 hour is equal to 3600 seconds.

Speed = 45 km/h
Speed = (45 * 1000) / 3600
Speed = 12.5 m/s

Now, we can calculate the RPM using the formula above:

RPM = (Speed / Circumference) * 60
RPM = (12.5 / 4.5) * 60
RPM = (2.78) * 60
RPM ≈ 166.7

Therefore, the wheel must make approximately 166.7 rotations per minute to achieve a speed of 45 km/h.