Respuesta :
Answer:
torque = 1.467 Nm
angle = 43.9275 radian
work = 64.442 J
average power = 42.961W
Explanation:
The three equations of rotational motion with uniform angular acceleration are,
ω = ω₀ + αt
θ = ω₀t + [tex]\frac{1}{2}[/tex][tex]\alpha t^{2}[/tex]
ω[tex]^{2}[/tex] = ω₀[tex]^{2}[/tex] + 2αθ
where,
ω₀ = initial angular velocity
ω = final angular velocity
α = angular acceleration
θ = angular displacement
Given that rotational inertia, I = 0.140 kg[tex]m^{2}[/tex]
We know that,
angular momentum, L = Iω
therefore,
ω = [tex]\frac{L}{I}[/tex]
initial angular momentum = 3.00 kg[tex]m^{2}[/tex]/s
initial angular velocity = [tex]\frac{initial angular momentum}{rotational momentum}[/tex] = [tex]\frac{3.00}{0.140}[/tex] = 21.428 /s
final angular momentum = 0.8 kg[tex]m^{2}[/tex]/s
final angular velocity = tex]\frac{final angular momentum}{rotational momentum}[/tex] = [tex]\frac{0.8}{0.140}[/tex] = 5.714 /s
time, t = 1.5 s
Now we have to find angular acceleration. For that we have initial and final angular velocities. The equation connecting these three quantities is
ω = ω₀ + αt
i.e. α = (ω - ω₀)/t
substituting the values,
α = [tex]\frac{21.428 - 5.714}{1.5}[/tex] = 10.476 /s[tex]^{2}[/tex]
We know that, torque = Iα
Substituting values,
torque = 0.140 x 10.476 = 1.467 Nm
Next we have to find the angle through which the flywheel turns. For that we have initial angular velocity, final angular velocity, angular acceleration and time. We have two equations connecting angle and the above mentioned quantities. Here, we are taking the equation,
θ = ω₀t + [tex]\frac{}{2}[/tex][tex]\alpha t^{2}[/tex]
substituting values,
θ = 21.428 x 1.5 + [tex]\frac{1}{2}[/tex] x [tex]10.476 X 1.5^{2}[/tex]
θ = 43.9275 radian
Now we have to find work done. For that we know that
Work done = torque x angle
substituting the values,
work done = 1.467 x 43.9275 = 64.442 J
We know that the average power = [tex]\frac{work done}{time}[/tex]
substituting the values,
average power = [tex]\frac{64.442}{1.5}[/tex] = 42.961W
