a wheel with an angular velocity of 300. rev/min increases to 500. rev/min in 10.0 sec. what is the angular acceleration the wheel is traveling?
200 *2 pi radians / 60 s = 20.9 radians/s change in omega
d omega /dt = alpha = 20.9/10 = 2.09 rad/s^2
To find the angular acceleration of the wheel, we can use the formula:
Angular acceleration (α) = Change in angular velocity (Δω) / Change in time (Δt)
First, let's calculate the change in angular velocity (Δω). We are given that the initial angular velocity (ωi) is 300 revolutions per minute (rev/min), and the final angular velocity (ωf) is 500 rev/min. Since angular velocity is measured in radians per second (rad/s), we need to convert the values to rad/s.
1 revolution = 2π radians
Initial angular velocity (ωi) = 300 rev/min
Convert ωi to rad/s: ωi = (300 rev/min) * (2π rad/1 rev) * (1 min/60 s) = 10π rad/s
Final angular velocity (ωf) = 500 rev/min
Convert ωf to rad/s: ωf = (500 rev/min) * (2π rad/1 rev) * (1 min/60 s) = 50π rad/s
Now we can calculate the change in angular velocity (Δω):
Δω = ωf - ωi
Δω = (50π rad/s) - (10π rad/s) = 40π rad/s
Next, we need to calculate the change in time (Δt), which is given as 10.0 seconds.
Now, using the formula for angular acceleration:
Angular acceleration (α) = Δω / Δt
α = (40π rad/s) / (10.0 s) = 4π rad/s²
Therefore, the angular acceleration of the wheel is 4π rad/s².