A turntable reaches an angular speed of 45.0 rpm in 2.21 s, starting from rest. Assuming the angular acceleration is constant, what is its magnitude?

To solve this problem, we first need to convert the angular speed from revolutions per minute (rpm) to radians per second, since the standard unit of angular speed in physics is rad/s.

1 revolution is equal to 2π radians, and 1 minute is equal to 60 seconds. So, 45.0 rpm is equal to:

45.0 rev/min * (2π rad/rev) * (1 min/60 s) = 4.71 rad/s

Next, we use the formula for angular acceleration, which is the change in angular speed divided by the change in time. In this case, the initial angular speed is 0 (since the turntable starts from rest), so the change in angular speed is just the final angular speed.

So, the angular acceleration (α) is:

α = Δω/Δt = (ω_final - ω_initial) / Δt = (4.71 rad/s - 0 rad/s) / 2.21 s = 2.13 rad/s²

So, the magnitude of the angular acceleration is 2.13 rad/s².