Answer :
The net torque required to accelerate is 28496 Nm.
What is the net torque required to accelerate it?
The net torque required to accelerate a uniform disk of radius 7.5 m and mass 29000 kg from rest to 0.63 rad/s in 27 s is needed.
The problem is asking for the net torque required to accelerate a merry-go-round from rest to a final angular velocity of 0.63 rad/s in 27 seconds. The merry-go-round is assumed to be a uniform disk, which means that its mass is evenly distributed across its entire radius. We are also given the radius of the merry-go-round (7.5 m) and its mass (29000 kg).
To solve the problem, we can use the formula:
[tex]τ = Iα[/tex]
where τ is the net torque applied to the merry-go-round, I is its moment of inertia, and α is its angular acceleration. Since the merry-go-round is initially at rest, its initial angular velocity is zero. Using the formula for angular acceleration, we can find that:
[tex]α = Δω/Δt = (0.63 rad/s - 0 rad/s) / 27 s = 0.0233 rad/s^2[/tex]
To find the moment of inertia of the merry-go-round, we can use the formula for the moment of inertia of a uniform disk:
[tex]I = (1/2)mr^2[/tex]
where m is the mass of the disk and r is its radius. Substituting the given values, we get:
[tex]I = (1/2)(29000 kg)(7.5 m)^2 = 1220625 kg m^2[/tex]
Finally, we can use the formula [tex]τ = Iα[/tex] to find the net torque required to accelerate the merry-go-round:
[tex]τ = (1220625 kg m^2)(0.0233 rad/s^2) = 28496 Nm[/tex]
Therefore, the net torque required to accelerate the merry-go-round is 28496 Nm.
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