Problem: Dario, a prep cook at an Italian restaurant, spins a salad spinner 20.0 times in 5.00 seconds and then stops spinning it. The salad spinner rotates 6.00 more times before it comes to rest. Assume that the spinner slows down with constant angular acceleration.1. What is the angular acceleration of the salad spinner as it slows down?2. How long does it take for the salad spinner to come to rest? (s)

FREE Expert Solution

We'll use the kinematic expression:

$\boxed{{{\mathbf{\omega }}_{\mathbf{f}}}^{\mathbf{2}}\mathbf{=}{{\mathbf{\omega }}_{\mathbf{0}}}^{\mathbf{2}}\mathbf{+}\mathbf{2}\mathbf{\alpha }\mathbf{\theta }}$

1. Solving for α:

$\boxed{\mathbf{\alpha }\mathbf{=}\frac{{{\mathbf{\omega }}_{\mathbf{f}}}^{\mathbf{2}}\mathbf{-}{{\mathbf{\omega }}_{\mathbf{0}}}^{\mathbf{2}}}{\mathbf{2}\mathbf{\theta }}}$

Angular velocity:

$\boxed{\mathbf{\omega }\mathbf{=}\frac{\mathbf{\theta }}{\mathbf{t}}}$

Angular displacement:

$\boxed{\mathbf{\theta }\mathbf{=}\mathbf{n}\mathbf{2}\mathbf{\pi }}$

Therefore, initial angular velocity:

ω₀ = (n2π)/t = (20)(2π)/5.00 = 8π rad/s

θ = (6.00)(2π) = 12π