# Physics GRE-Classical Mechanics-Rotational Motion about A Fixed Axis

### 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

$$I_t=I_{com}+mr^2$$

#### 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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