Determine the change in rotational kinetic energy when the rotational velocity of the turntable of a stereo system increases from 0 to 33 rpm. Its rotational inertia is 6.8×10−3kg⋅m2 .
To determine the change in rotational kinetic energy, we need to use the formula for rotational kinetic energy:
K = (1/2) * I * ω^2
where K represents the rotational kinetic energy, I is the rotational inertia, and ω is the angular velocity.
The given information states that the initial angular velocity is 0. We can use this value to calculate the initial rotational kinetic energy, K_initial.
K_initial = (1/2) * I * ω_initial^2
Since ω_initial is 0, the initial rotational kinetic energy is 0.
Now, we need to calculate the final rotational kinetic energy, K_final, when the rotational velocity increases to 33 rpm. To do this, we first need to convert the final angular velocity from rpm to rad/s.
To convert rpm to rad/s, we multiply the angular velocity by (2π/60).
Angular velocity in rad/s = 33 rpm * (2π/60) = (33 * 2π)/60 = (33π)/60 rad/s
Now, we can calculate the final rotational kinetic energy.
K_final = (1/2) * I * ω_final^2
K_final = (1/2) * (6.8×10−3 kg⋅m^2) * [(33π)/60]^2
Calculate the value to find the change in rotational kinetic energy.