If, after rotating for some time at constant angular velocity of 72 rad/s, brakes are applied to the flywheel
producing retardation of 4 rad/s2
, determine the time taken to reduce its angular velocity to 40 rad/s.
V = Vo + a*t
V = 40 rad/s
Vo = 72 rad/s
a = -4 rad/s^2
Solve for t
16 sec
To determine the time taken to reduce the angular velocity of the flywheel, we can use the formula for angular acceleration:
Angular acceleration (α) = change in angular velocity (Δω) / time taken (Δt)
Given:
Initial angular velocity (ω1) = 72 rad/s
Final angular velocity (ω2) = 40 rad/s
Angular acceleration (α) = -4 rad/s² (negative sign because the angular velocity is decreasing)
We need to calculate the time taken (Δt).
Rearranging the formula, we have:
Δt = Δω / α
Substituting the given values:
Δt = (ω2 - ω1) / α
Δt = (40 rad/s - 72 rad/s) / -4 rad/s²
Δt = -32 rad/s / -4 rad/s²
Δt = 8 s
Therefore, it will take 8 seconds to reduce the angular velocity of the flywheel from 72 rad/s to 40 rad/s.