• Scalar: Quantity with magnitude only (no direction)
• Examples: distance, speed, mass, time, energy
• Added/subtracted using ordinary arithmetic

...

• Graphical method: Tip-to-tail method
• Addition: Place tail of second vector at tip of first
• Resultant: From tail of first to tip of last

...

• Object: Single rigid body
• System: Collection of objects that can move together or separately
• Can treat system as single object located at center of mass

...

• $x_{cm} = \frac{m_1x_1 + m_2x_2 + ...}{m_1 + m_2 + ...}$
• $y_{cm} = \frac{m_1y_1 + m_2y_2 + ...}{m_1 + m_2 + ...}$
• For continuous objects: $x_{cm} = \frac{1}{M}\int x\,dm$

...

$W = Fd\cos\theta$

• Force must have component parallel to displacement
• Positive work: force has component in direction of motion

...

• $W = \int F_x\,dx$ (variable force)
• Graphically: Area under F vs. position curve
• Spring force: $W = \int_0^x kx'\,dx' = \frac{1}{2}kx^2$

...

$\vec{p} = m\vec{v}$

• Vector quantity (direction same as velocity)
• Proportional to mass and velocity

...

$\vec{J} = \vec{F}_{avg}\Delta t = \Delta\vec{p}$

• Vector quantity (direction of net force)
• Change in momentum over time interval

...

• Angular displacement ($\theta$): Radian measure of rotation angle
• Angular velocity ($\omega$): $\omega = \frac{d\theta}{dt}$ (rad/s)
• Angular acceleration ($\alpha$): $\alpha = \frac{d\omega}{dt} = \frac{d^2\theta}{dt^2}$ (rad/s2))))

$\omega = \omega_0 + \alpha t$ $\theta = \theta_0 + \omega_0 t + \frac{1}{2}\alpha t^2$ $\omega^2 = \omega_0^2 + 2\alpha\Delta\theta$

...

$K_{rot} = \frac{1}{2}I\omega^2$

• Energy of rotation
• Depends on moment of inertia and angular velocity

...

$K_{total} = K_{trans} + K_{rot} = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2$

• For rolling without slipping: $v = r\omega$
• $K = \frac{1}{2}mv^2 + \frac{1}{2}(mr^2)\left(\frac{v}{r}\right)^2 = \frac{1}{2}mv^2\left(1 + \frac{I}{mr^2}\right)$

...

• Periodic motion back and forth over same path
• Restoring force proportional to displacement from equilibrium
• $F_{restoring} = -kx$ (Hooke's law type force)

...

• Force directed toward equilibrium position
• Proportional to displacement: $F = -kx$
• Causes oscillation about equilibrium

...

$\rho = \frac{m}{V}$

• Mass per unit volume
• Units: kg/m3

...

$P = \frac{F}{A}$

• Force per unit area
• Units: Pa (Pascal) = N/m2

...