14. A boy is riding a bicycle at a velocity of 4 m/s. The bicycle's whel'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) To find the velocity of a point on the rim of the wheel, we can use the formula:
v = ωr
where v is the linear velocity, ω is the angular velocity, and r is the radius of the wheel.
Given that the velocity is 4 m/s and the diameter of the wheel is 0.8 m, we can find the radius by dividing the diameter by 2:
r = 0.8 m / 2 = 0.4 m
Substituting the values into the formula, we have:
4 m/s = ω * 0.4 m
ω = 4 m/s / 0.4 m
ω = 10 rad/s
Therefore, the velocity of a point on the rim of the wheel is 10 rad/s.
b) The angular displacement of the wheel can be calculated by using the formula:
θ = (number of revolutions) * (2π radians/revolution)
Given that the number of revolutions is 40, we have:
θ = 40 * (2π radians/revolution)
θ = 80π radians
The angular velocity of the wheel can be calculated by using the formula:
ω = θ / t
where t is the time taken to complete the given number of revolutions. Since the time is not given, we cannot calculate the exact angular velocity.
c) The angular acceleration of a point on the rim of the wheel can be calculated using the formula:
α = Δω / Δt
where Δω is the change in angular velocity and Δt is the change in time.
Since the time and change in angular velocity are not provided, we cannot calculate the exact angular acceleration.