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.
c) what is the angular acceleration of a point on the rim of the wheel?
To find the angular acceleration of a point on the rim of the wheel, we first need to find the angular velocity.
The angular velocity (ω) can be calculated using the formula:
ω = v / r
where v is the linear velocity and r is the radius (half of the diameter) of the wheel.
Given that the linear velocity (v) is 4 m/s and the diameter is 0.8 m, the radius (r) would be 0.8 m / 2 = 0.4 m.
Substituting these values into the formula, we get:
ω = 4 m/s / 0.4 m
= 10 rad/s
Now, we can find the number of revolutions (N) using the formula:
N = (ω * t) / (2π)
where t is the time to complete the given number of revolutions.
Given that the number of revolutions is 40, we can rearrange the formula to solve for t:
t = (N * 2π) / ω
Substituting the values into the formula, we get:
t = (40 * 2π) / 10 rad/s
≈ 25.13 s
Now, we can find the angular acceleration (α) using the formula:
α = Δω / Δt
where Δω is the change in angular velocity and Δt is the change in time.
Since the wheel is rotating at a constant velocity, there is no change in angular velocity (Δω = 0). Therefore, the angular acceleration (α) would be 0 rad/s^2.