The angular acceleration of the wheel is determined as 40 rad/s². (Option C).
How to calculate the angular acceleration of the wheel?
The angular acceleration of the wheel is calculated by applying the following formulas as shown below.
α = Δω / Δ t
α = ( ω₂ - ω₁ ) / t
where;
- ω₂ is the final angular speed
- ω₁ is the initial angular speed
- t is the time of motion
The given parameters is as follows;
the final angular speed, ω₂ = 4500 rev/min x 2π rad/rev x 1 min / 60 s
ω₂ = 471.24 rad/s
the initial angular speed, ω₁ = 1200 rev/min x 2π rad/rev x 1 min / 60 s
ω₁ = 125.66 rad/s
The angular acceleration of the wheel is calculated as;
α = ( ω₂ - ω₁ ) / t
α = ( 471.24 - 125.66 ) / 10 s
α = 34.56 rad/s²
α ≈ 40 rad/s²