a. 28.9rad/s * 1rev/6.28rad = 4.60 rev/s.
t = (13.6/4.60) * 1s = 3.0 s.
b. V = Vo + at = 0 When @ rest.
28.9 + a*3 = 0
3a = -28.9
a = -9.63 rad/s^2.
t = (13.6/4.60) * 1s = 3.0 s.
b. V = Vo + at = 0 When @ rest.
28.9 + a*3 = 0
3a = -28.9
a = -9.63 rad/s^2.
writing the correct way to help others:
rev *6.28 = rads
t= 2 *rads/angular velocity
a = angular velocity/2*rads = - (Answer)
ω = Δθ / Δt
where ω is the angular velocity, Δθ is the angular displacement, and Δt is the time it takes.
(a) We are given that the angular velocity of each wheel is 28.9 rad/s, and the angular displacement of each wheel is 13.6 revolutions.
Converting the angular displacement from revolutions to radians:
13.6 revolutions * 2π radians/revolution = 13.6 * 2π radians ≈ 85.942 radians
Now, we can rewrite the formula as:
28.9 rad/s = 85.942 radians / Δt
Solving for Δt:
Δt = 85.942 radians / 28.9 rad/s ≈ 2.974 seconds
Therefore, it takes approximately 2.974 seconds for the bike to come to rest.
(b) To find the angular acceleration, we can use the formula:
α = Δω / Δt
where α is the angular acceleration, Δω is the change in angular velocity, and Δt is the time it takes.
Since the bike comes to a stop, the final angular velocity is 0 rad/s and the initial angular velocity is 28.9 rad/s.
Substituting the values:
α = (0 rad/s - 28.9 rad/s) / 2.974 seconds ≈ -9.713 rad/s^2
The angular acceleration of each wheel is approximately -9.713 rad/s^2. (Note: the negative sign indicates deceleration.)
(a) To find the time it takes for the bike to come to rest, we can use the formula:
time = angular displacement / angular velocity
Given:
Angular velocity (ω) = 28.9 rad/s
Angular displacement (θ) = 13.6 revolutions
First, let's convert the angular displacement from revolutions to radians:
1 revolution = 2Ï€ radians
So, 13.6 revolutions = 13.6 * 2Ï€ radians
Plug the values into the formula:
time = (13.6 * 2Ï€ radians) / 28.9 rad/s
Now we can calculate the time it takes for the bike to come to rest.
(b) To find the angular acceleration of each wheel, we can use the formula:
angular acceleration = change in angular velocity / time
Since the bike comes to rest, the final angular velocity is 0 rad/s.
Therefore, change in angular velocity (Δω) = final angular velocity - initial angular velocity = 0 - 28.9 rad/s = -28.9 rad/s
Now, we can use the formula to calculate the angular acceleration:
angular acceleration = (-28.9 rad/s) / time (from part a)
By plugging the value of time obtained in part a, you can calculate the angular acceleration of each wheel in rad/s².