Final answer:
To find the angular acceleration of the turntable, use the equation α = (ωf - ωi) / t. For the number of revolutions made while stopping, use θ = ωi * t + (1/2) * α * t^2.
Step-by-step explanation:
In order to determine the angular acceleration of the turntable, we need to use the equation:
ωf - ωi = αt
where:
- ωf is the final angular velocity, which is 0 since the turntable stops
- ωi is the initial angular velocity, which can be calculated as 2π times the initial rotational frequency (33 1/3 rev/min)
- α is the angular acceleration we're trying to find
- t is the time taken for the turntable to stop (1.0 min)
Plugging in these values, we can solve for α by rearranging the equation:
α = (ωf - ωi) / t
For part (b), we can use the equation:
θ = ωi * t + (1/2) * α * t^2
where:
- θ is the total angle covered by the turntable while stopping
- ωi is the initial angular velocity
- t is the time taken for the turntable to stop
- α is the angular acceleration