Question

Dario, a prep cook at an Italian restaurant, spins a salad spinner and observes that it rotates 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.

Answer 1

Answer:

(a). The acceleration is 8.3 rad/s².

(b). The time is 3.0 sec.

Explanation:

Given that,

Rotation = 20.0 times

Time = 5.00 sec

We need to calculate the angular frequency

Using formula of angular frequency

$\omega_{i}=20\times\dfrac{2\pi}{T}$

put the value into the formula

$\omega_{i}=20\times\dfrac{2\pi}{5.00}$

$\omega_{i}=8.00\pi$

We need to calculate the angular displacement

Using formula of  angular displacement

$\theta=6\times2\pi=12\pi$

We need to calculate the angular acceleration

Using equation of angular motion

$\omega_{f}^2-\omega_{i}^2=2\alpha\times\theta$

$0-64\pi^2=2\times12\pi\times\alpha$

$\alpha=-\dfrac{64\pi^2}{24\pi}$

$\alpha=-8.3\ rad/s^2$

Negative sign shows the opposite direction of the motion.

The acceleration is 8.3 rad/s².

We need to calculate the time

Using equation of angular motion

$\omega_{f}-\omega_{i}=\alpha\times t$

$0-8\pi=-8.3t$

$t=\dfrac{8\pi}{8.3}$

$t=3.0\ sec$

The time is 3.0 sec.

Hence, (a). The acceleration is 8.3 rad/s².

(b). The time is 3.0 sec.