Angular acceleration is defined as the change of angular velocity with respect to time. The angular velocity of a turntable in motion with constant angular acceleration α is equal to [tex]\omega&=\sqrt{\alpha\times\pi[/tex].
Given that,
The angular acceleration is = α
From the second equation of motion, we have:
Since the turntable is in motion, the initial velocity becomes zero, such that:
[tex]\theta&=\dfrac{1}{2} \alpha \text t^{2}[/tex]......................(1)
Also, we know that angular velocity is equal to:
[tex]\omega &=\dfrac{\theta}{\text t}[/tex] ..........................(2)
Substituting the equation 1 into 2, we get:
[tex]\omega &=\dfrac {\dfrac{1}{2} \alpha \text t^{2}}{\text t}\\\omega&=\dfrac{1}{2} \alpha\times \text t[/tex] ..........................(3)
Since,
[tex]\text t &=\dfrac{\alpha\pi}{\omega}[/tex]
Putting the value in equation (3),
[tex]\omega&=\dfrac{1}{2} \alpha\times\dfrac{2 \pi}{\omega}\\\\\omega^2&=\alpha\times\pi\\\\\omega&=\sqrt{\alpha\times\pi[/tex]
Therefore, the angular velocity will be equal to [tex]\omega&=\sqrt{\alpha\times\pi[/tex].
To know more about angular velocity, refer to the following link:
https://brainly.com/question/13944035
