Answer:
[tex]-\frac{8\pi}{3}rad/s^2[/tex]
Explanation:
To solve this problem we need to apply the concept related to Angular Acceleration. We can find it through the equation
[tex]\omega_f^2-\omega_i^2=2\alpha\theta[/tex]
Where for definition,
[tex]\omega_i = \frac{\theta}{t}[/tex]
The number of revolution [tex](\theta)[/tex]was given by 20 times, then
[tex]\omega_i = \frac{20*2pi}{5}[/tex]
[tex]\omega = 8\pi rad/s[/tex]
We know as well that the salad rotates 6 more times, therefore in angle measurements that is
[tex]\theta = 6*2\pi rad = 12\pi rad[/tex]
The cook at the end stop to spin, then using our first equation,
[tex]0-8\pi = 2\alpha (12\pi)[/tex]
re-arrange to solve[tex]\alpha[/tex] ,
[tex]\alpha = \frac{-8\pi}{2*12\pi}[/tex]
[tex]\alpha = -\frac{8\pi}{3}rad/s^2[/tex]
We can know find the required time,
[tex]\omega_f-\omega_i = \alpha t[/tex]
Re-arrange to find t, and considering that [tex]\omega_f=0[/tex]
[tex]t= \frac{\omega_i}{\alpha}[/tex]
[tex]t=\frac{-8\pi}{-8\pi/3}[/tex]
[tex]t=3s[/tex]
Therefore take for the salad spinner to come to rest is 3 seconds with acceleration of [tex]-\frac{8\pi}{3}rad/s^2[/tex]
Answer:
-480.1°/s²
Explanation:
The angular acceleration (α) can be calculated using the following equation:
[tex]\alpha = \frac{\omega_{f}^{2} - \omega_{0}^{2}}{2*\Delta \theta}[/tex]
Where:
[tex]\omega_{f}[/tex]: is the final angular speed = 0
[tex]\omega_{0}[/tex]: is the initial angular speed
Δ[tex]\theta_[/tex]: is the angular displacement
The initial angular speed (ω₀) can be calculated as follows:
[tex] \omega_{0} = \frac{\theta_{0}}{t} [/tex]
Where t is the time = 5.00 s
[tex] \omega_{0} = \frac{\theta_{0}}{t} = \frac{20 rev*\frac{2\pi rad}{1 rev}}{5 s} = 25.13 rad/s [/tex]
Now, we can find the angular acceleration:
[tex]\alpha = \frac{\omega_{f}^{2} - \omega_{0}^{2}}{2*\Delta \theta} = - \frac{(25.13 rad/s)^{2}}{2*(6 rev*(\frac{2\pi rad}{1 rev}))} = - 8.38 rad/s^{2}[/tex]
[tex] \alpha = -8.38 rad/s^{2}*\frac{360 ^\circ}{2\pi rad} = -480.1 ^\circ/s^{2} [/tex]
Therefore, the angular acceleration is -480.1°/s².
I hope it helps you!
