Answer:
35%
Explanation:
Assuming no external torques present during the collision between the record and the turntable, total angular momentum must be conserved.
For a rotating body with some angular velocity and moment of inertia, the angular momentum can be expressed as follows;
L = I* ω
So, as initial angular momentum and final angular momentum must be the same, we have:
Li = Lf
⇒ I₁ * ω₁ = I₂ * ω₂ (1)
where I₁ is the rotational inertia of the turntable, and I₂, is the combined rotational inertia of the turntable and the record:
I₂ = I₁ + 0.54 I₁ = 1.54 I₁
We can solve (1) for the new common angular speed, as follows:
ω₂ = ω₁ / 1.54 (2)
The initial rotational kinetic energy is given by definition for the following equation:
Kroti = 1/2 * I₁ * ω₁² (3)
The final rotational kinetic energy takes into account the new rotational inertia and the common final angular speed:
Krotf = 1/2* I₂ * ω₂² = 1/2* 1.54 I₁* (ω₁/1.54)² (4)
Dividing both sides in (3) and (4), we get:
Krotf/Kroti = 1/1.54 = 0.65
This means that the final rotational kinetic energy, has reduced to 0.65 of the initial value, or that has lost 35% of the initial kinetic energy.
