Respuesta :
Answer:
Angular displacement will be [tex]\frac{1}{4}\Theta[/tex]
So option (b) will be the correct option
Explanation:
We have given that firstly object is at rest
So [tex]\omega _i=0rad/sec[/tex]
From law of motion we know that angular displacement is given by
[tex]\Theta =\omega _it+\frac{1}{2}\alpha t^2=0\times t+\frac{1}{2}\alpha t^2=\frac{1}{2}\alpha t^2[/tex]
Now angular displacement by the object in [tex]\frac{t}{2}sec[/tex]
[tex]\Theta =0\times t+\frac{1}{2}\alpha (\frac{t}{2})^2=\frac{1}{4}(\frac{1}{2}\alpha t^2)=\frac{1}{4}\Theta[/tex]
So option (b) will be the correct option
The angle the object rotate through in the time [tex]\frac{1}{2} t[/tex] is [tex]\frac{1}{4} (\theta)[/tex]
Given the following data:
- Initial angular speed = 0 m/s (since it starts from rest).
- Angle = [tex]\theta[/tex]
- Time = t
To determine the angle the object rotate through in the time [tex]\frac{1}{2} t[/tex]:
How to calculate angular displacement.
Mathematically, angular displacement is given by this formula:
[tex]\theta = \omega_i t +\frac{1}{2} \alpha t^2[/tex]
Where:
- [tex]\theta[/tex] is the angular displacement.
- [tex]\omega[/tex] is the initial angular speed.
- [tex]\alpha[/tex] is the angular acceleration.
- t is the time.
Substituting the given parameters into the formula, we have;
[tex]\theta = 0( t )+\frac{1}{2} \alpha t^2\\\\\theta = \frac{1}{2} \alpha t^2[/tex]
when t = [tex]\frac{1}{2} t[/tex]:
[tex]\theta = \frac{1}{2} \alpha (\frac{t}{2} )^2\\\\\theta = \frac{1}{2} \alpha (\frac{t^2}{4} )\\\\\theta =\frac{1}{4} (\frac{1}{2} \alpha t^2)\\\\\theta =\frac{1}{4} (\theta)[/tex]
Read more on angular speed here: https://brainly.com/question/6860269
