Problems
PGRE1777(48, 65)
PGRE9677(21, 32)
PGRE9277(8, 40, 41, 42, 78, 82, 100)
PGRE8677(76, 96)
PGRE0177(25, 26, 75, 89, 91)
Formulas
Angular Velocity
$$\omega=\frac{v}{r}$$
Angular Acceleration
$$\alpha=\frac{a}{r}$$
Rotational Inertia(Moment of Inertia)
$$I=mr^2$$
Parallel Axis Theorem
$$I_t=I_{com}+mr^2$$
Memorizing Rotational Inertia for Each Shape
Kinetic Energy for Rotation
$$KE_{rot}=\frac{1}{2}I \omega^2$$
Total Kinetic Energy
$$KE_t=KE_{trans}+KE_{rot}$$
Torque
$$\tau=I \alpha=\frac{\omega_f-\omega_i}{\Delta t}=r×F$$
Period for Physical Pendulum
$$T=2\pi \sqrt{ \frac{I}{mgd}}$$
Angular Momentum
$$L=rmv=I\omega=r×p=m(r×v)$$
Total Angular Momentum
$$L_t=L_{trans}+L_{rot}$$
Matrix for Rotation about Z Axis
$$
\begin{pmatrix}
\cos{\theta} & -\sin{\theta} & 0\\
\sin{\theta} & \cos{\theta} & 0\\
0 & 0 &1\\
\end{pmatrix}
$$
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