Respuesta :
Answer:
d. a2 = 9a1
Explanation:
We can apply the following equation of motion to calculate the angular acceleration:
[tex]\omega^2 - \omega_0^2 = 2\alpha\theta[/tex]
Since both wheel starts from rest, their [tex]\omega_0 = 0 rad/s[/tex]
[tex]\omega^2 = 2\alpha\theta[/tex]
We can take the equation for the 1st wheel, divided by the equation by the 2nd wheel:
[tex]\frac{\omega_1^2}{\omega_2^2} = \frac{2\alpha_1\theta_1}{2\alpha_2\theta_2}[/tex]
As they were rotating through the same angular displacement [tex]\theta_1 = \theta_2[/tex], these 2 cancel out
[tex]\left(\frac{\omega_1}{\omega_2}\right)^2 = \frac{\alpha_1}{\alpha_2}[/tex]
[tex]\left(\frac{1}{3}\right)^2 = \frac{\alpha_1}{\alpha_2}[/tex]
[tex]\frac{1}{9} = \frac{\alpha_1}{\alpha_2}[/tex]
[tex]\alpha_2 = 9\alpha_1[/tex]
So d is the correct answer
The angular acceleration of the first wheel is four times higher than that of the second. Option D is correct.
What is angular acceleration?
It can be defined as the rate of change in the angular velocity of an object or body. It can be calculated by the equation of motion:
[tex]\omega ^2 - \omega _0^2 = 2\alpha \theta[/tex]
Since initial angular rotation is zero for both the wheels,
[tex]\omega ^2 = 2\alpha \theta[/tex]
Compare the angular acceleration of both wheels,
[tex]\dfrac {\omega_1^2}{\omega_2^2} = \dfrac {2\alpha_1 \theta}{2\alpha_2\theta }[/tex]
Put the values,
[tex]\begin{aligned} (\dfrac 13)^2&= \dfrac {\alpha_1 }{\alpha_2 }\\\\ \dfrac 19 &= \dfrac {\alpha_1 }{\alpha_2 }\\\\\alpha_2 &= 9\alpha_1 \end {aligned}[/tex]
Therefore, The angular acceleration of the first wheel is four times higher than that of the second. Option D is correct.
To know more about angular acceleration,
https://brainly.com/question/13071907
