Question

prove torque = i alpha

Answer 1

here is your answer ⤵️

according to Newton's second law.

➡️ ∑F = ma

➡️ ∑r × F = mr × a

➡️ ∑r × F = mr × (α × r)

➡️ ∑r × F = mα(r · r) − r(r · α)

➡️ ∑r × F = mαr² − 0

➡️ ∑r × F = mr²α

➡️ ∑τ = Iα

__hope it help ✌️

Answer 2

Torque = I × angular acceleration

Proof :

Torque will be defined as the rate change of angular momentum with respect to time.

$\tau = \dfrac{d L}{dt}$

• $\tau$ is torque, L is angular momentum and t is time.

• Angular momentum is written as $I\times\omega$ , where $\omega$ is angular velocity.

$\implies \tau = \dfrac{d (I \times \omega)}{dt}$

$\implies \tau =I \times \dfrac{d \omega}{dt}$

$\implies \tau =I \times \alpha$

• $\alpha$ is angular acceleration.

[Hence derived].