AP Physics 1 new eqs

Angular Momentum

L=Iω

\omega = \omega_0 + \alpha t

The rotational kinematics equation for angular velocity as a function of time, under constant angular acceleration.

\Delta \theta = \omega_0 t + \frac{1}{2}\alpha t^2

The rotational kinematics equation for angular displacement as a function of time, involving initial angular velocity and constant angular acceleration.

\omega^2 = \omega_0^2 + 2\alpha \Delta \theta

The rotational kinematics equation relating angular velocity to angular displacement, independent of time.

Tangential Velocity and Angular Velocity

The relationship between linear and rotational speed for a point at radius r, expressed as v = r\omega.

Tangential Acceleration and Angular Acceleration

The relationship between linear tangential acceleration and angular acceleration, expressed as a_t = r\alpha.

Centripetal Acceleration (a_c)

The inward acceleration of an object in circular motion, expressed in terms of angular velocity as a_c = \omega^2 r.

Period (T)

The time taken for one full rotation or cycle, calculated as T = \frac{2\pi}{\omega}.

Frequency (f)

The number of rotations or cycles per unit time, often measured in Revolutions Per Second (rev/s) or Hertz (Hz).

Relationship between Period and Frequency

The reciprocal interaction between the time for one cycle and the number of cycles per second: T = \frac{1}{f}.

torque eq

τ = rFsinθ

Rotational Newton’s 2nd Law

∑τ = Iα

rotational inertia eq

I=∑mi​ * ri^2​

Parallel Axis Theorem

I=Icm​+Md^2

Rotational kinetic energy

Krot​ = (1/2)*​I*ω^2

Angular impulse

ΔL=τΔt