14. A boy is riding a bicycle at a velocity of 4 m/s. The bicycle's wheel's have a diameter of 0.8
m and 40 revolutions.
a) what is the velocity of a point on the rim of the wheel?
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?
a) The velocity of a point on the rim of the wheel can be calculated using the formula:
velocity = angular velocity x radius
The diameter of the wheel is given as 0.8 m, so the radius is half of that, which is 0.4 m.
Since the wheel has a diameter of 0.8 m, the circumference of the wheel is πd or 2πr, which is 2π(0.4) = 2.5 m.
The number of revolutions is given as 40.
The time it takes to complete 40 revolutions can be calculated by dividing the number of revolutions by the number of revolutions per second, which is given by the velocity of the bicycle (4 m/s).
Time = Number of revolutions / Revolutions per second
Time = 40 / (2.5/4)
Time = 40 / 1.6
Time = 25 seconds
So, in 25 seconds, the point on the rim of the wheel would have traveled the circumference of the wheel, which is 2.5 m.
Therefore, the velocity of the point on the rim of the wheel is 2.5 m / 25 s = 0.1 m/s.
b) The angular displacement of the wheel can be calculated using the formula:
angular displacement = (number of revolutions)(2π)
The number of revolutions is given as 40, so the angular displacement is:
angular displacement = 40(2π) = 80π rad
The angular velocity of the wheel can be calculated by dividing the angular displacement by the time taken to complete those revolutions.
angular velocity = angular displacement / time
angular velocity = 80π rad / 25 s
angular velocity ≈ 10π/25 rad/s
angular velocity ≈ 0.4 rad/s
c) The angular acceleration can be calculated using the formula:
angular acceleration = (change in angular velocity) / time
Since the angular velocity was constant, the change in angular velocity is 0, so the angular acceleration is 0 rad/s^2.