the wheel of bicycle has radius of 40cm . calculate its period of revolution if the bicycle moves with a speed of 20 km/h . how much is the angular velocity
To find the period of revolution, we need to first calculate the circumference of the wheel. The circumference of the wheel is given by 2πr, where r is the radius of the wheel.
Circumference = 2π(40 cm) = 80π cm.
Next, we need to convert the speed from km/h to cm/s. There are 100,000 cm in 1 km and 3600 seconds in 1 hour, so the speed in cm/s is:
Speed = (20 km/h) * (100,000 cm/km) / (3600 s/h)
= (200,000/36) cm/s
= 5555.56 cm/s (rounded to 2 decimal places).
The period of revolution is the time it takes for one complete revolution, which can be calculated using the formula:
Period = Circumference / Speed
= (80π cm) / (5555.56 cm/s)
≈ 0.0455 seconds (rounded to 4 decimal places).
To find the angular velocity, we can use the formula:
Angular velocity = 2π / Period
= 2π / 0.0455 s
≈ 138.07 rad/s (rounded to 2 decimal places).
Therefore, the period of revolution is approximately 0.0455 seconds, and the angular velocity is approximately 138.07 rad/s.