Continue with the physics formula

here are more key formulas for advanced level physics, focusing on Rotational Dynamics:

11. Rotational Dynamics

• Angular Velocity: $$\omega = \frac{\Delta\theta}{\Delta t}$$
• Angular Acceleration: $$\alpha = \frac{\Delta\omega}{\Delta t}$$
• Rotational Kinematics (constant angular acceleration): $$\omega = \omega_0 + \alpha t$$ $$\theta = \omega_0 t + \frac{1}{2}\alpha t^2$$ $$\omega^2 = \omega_0^2 + 2\alpha\theta$$
• Torque: $$\tau = rF\sin\theta = I\alpha$$
• Moment of Inertia: $$I = \sum mr^2 \quad \text{(for point masses)}$$
• Rotational Kinetic Energy: $$E_k = \frac{1}{2}I\omega^2$$
• Angular Momentum: $$L = I\omega$$
• Conservation of Angular Momentum: $$I_1\omega_1 = I_2\omega_2$$

That covers the major areas of advanced level physics formulas.