After fixing a flat tire on a bicycle you give the wheel a spin. Its initial angular speed was 6.50 and it rotated 15.2 revolutions before coming to rest.What was its average angular acceleration?
without units attached to your numerals, there can be no sense made. 6.50 what? rad/sec? rev/sec?
0.427
To find the average angular acceleration, we can use the formulas of angular displacement and average angular acceleration.
The formula for angular displacement is:
Δθ = θf - θi
where:
Δθ is the angular displacement
θf is the final angle (in radians)
θi is the initial angle (in radians)
In this case, the wheel rotates 15.2 revolutions. Since 1 revolution is equivalent to 2π radians, we can convert the revolutions to radians:
θf = (15.2 revolutions) * (2π radians/1 revolution) = 30.4π radians
The initial angle is 0 radians because the wheel starts from rest:
θi = 0 radians
Substituting these values into the formula for angular displacement:
Δθ = 30.4π radians - 0 radians = 30.4π radians
The formula for average angular acceleration is:
α_avg = Δω/Δt
where:
α_avg is the average angular acceleration
Δω is the change in angular speed
Δt is the time interval
We are given the initial angular speed:
ωi = 6.50 rad/s
The final angular speed is 0 rad/s because the wheel comes to rest:
ωf = 0 rad/s
The change in angular speed can be calculated as:
Δω = ωf - ωi = 0 rad/s - 6.50 rad/s = -6.50 rad/s
As for the time interval (Δt), it is not provided in the question. Therefore, without this information, it is not possible to determine the average angular acceleration. The time interval is required to find the average angular acceleration.