Final answer:
The period of revolution for the bicycle wheel is 0.45 seconds, and the angular velocity of the wheel is 13.96 rad/s when the bicycle is moving at a speed of 20 km/h.
Step-by-step explanation:
Calculation of the Period of Revolution and Angular Velocity
To calculate the period of revolution for a bicycle wheel, we need to determine how long it takes for the wheel to make one complete rotation.
The bicycle moves with a speed of 20 km/h.
First, we convert this speed into meters per second (20 km/h = 5.56 m/s).
The circumference of the bicycle wheel is given by 2πr, where r is the radius of the wheel.
So the circumference is 2π × 0.4 m = 2.51 m.
The period T is the time it takes to cover this distance at the given speed, so T = circumference / speed
= 2.51 m / 5.56 m/s
= 0.45 seconds.
To find the angular velocity ω, we use the formula ω = 2π / T.
Substituting the period we found, ω = 2π / 0.45 s = 13.96 rad/s.
The angular velocity is the rate at which the wheel rotates, measured in radians per second, and the period of revolution is the duration of one complete cycle of rotation.