14. A boy is riding a bicycle at a velocity of 4 m/s. The bicycle's wheel's have a diameter of 0.8m and 40 revolutions.
b) Calculate the angular displacement and velocity of the wheel.
c) what is the angular acceleration of a point on the rim of the wheel?
To solve this problem, we need to use the formulas relating linear velocity, angular velocity, and angular displacement.
a) First, we will calculate the angular displacement (θ) of the wheel.
The distance covered by the wheel in one revolution is equal to the circumference of the wheel. The circumference can be calculated using the formula C = πd, where d is the diameter of the wheel.
C = π * 0.8m = 2.5m
So, in one revolution, the wheel covers a distance of 2.5 meters.
Since the wheel makes 40 revolutions, the total distance covered is 40 * 2.5 = 100 meters.
Now, we need to calculate the angular displacement.
Angular displacement (θ) = Linear distance / Radius
The linear distance covered is 100 meters, and the radius of the wheel is half of the diameter, which is 0.8/2 = 0.4 meters.
Therefore, the angular displacement (θ) = 100 meters / 0.4 meters = 250 radians.
b) Next, we will calculate the angular velocity (ω) of the wheel.
Angular velocity (ω) = Linear velocity / Radius
The linear velocity is given as 4 m/s, and the radius of the wheel is 0.4 meters.
Therefore, the angular velocity (ω) = 4 m/s / 0.4 meters = 10 radians/s.
c) Finally, we will calculate the angular acceleration (α) of a point on the rim of the wheel.
Angular acceleration (α) = Change in angular velocity / Time taken
Since the problem doesn't provide any information about the change in angular velocity or the time taken, it is not possible to calculate the angular acceleration.
Therefore, we cannot determine the angular acceleration without additional information.