AP Physics 1

AP Physics Classroom

S6 Physics Study Doc

1. Kinematics

Kinematics Equations

$$v_2=v_1+a\Delta t$$ $$\Delta d=v_{1}t+\frac{1}{2}a\Delta t^2$$ $$\Delta d=v_{2}t-\frac{1}{2}a\Delta t^2$$ $$v_2^2=v_1^2+2a\Delta d$$

2. Dynamics

Terminal Velocity (k = drag constant)

$$F_g=F_{drag}$$ $$F_g=mg$$ $$F_{drag}=kv$$

3. Circular Motion and Gravity

Circular Motion

$$F_{netC}=\frac{m{v}^2}{r}=\frac{G{m}_1{m}_2}{r}=\frac{m_{2}4{\pi }^{2}R}{t^2}$$

4. Energy

Mechanical = Kinetic + Potential

Energy

$$Work=F\Delta d\cos \theta$$ $$E_k=\frac{1}{2}m{v}^2$$ $$E_g=mg\Delta h$$ $$E_e=\frac{1}{2}k{x}^2$$ $$F_e=kx$$

• K = spring constant $\left(\frac{N}{m}\right)$
• x = spring extension / compression $(m^2)$

Energy of Mass Oscillating

$$E_{total}=\frac{1}{2}m(V_{max}{)}^2$$ $$T_{total}=\frac{1}{2}k{A}^2$$

• k = coefficient
• A = amplitude

$$E_{total}=E_{elastic}+E_{kinetic}$$

If amplitude is known:

$$E_{kinetic}=\frac{1}{2}k{A}^2-\frac{1}{2}k{x}^2$$

If $V_{max}$ is known:

$$\frac{1}{2}m(V_{max}{)}^2-\frac{1}{2}k{x}^2$$

Speed of mass at any point:

$$v=\sqrt{\frac{K(A^2-x^2)}{m}}$$

Forces and Collisions

Conservative vs Nonconservative

• Conservative Force: doesn’t depend on path
• Nonconservative Force: depends on path

Elastic vs Inelastic

• Elastic collision: Kinetic Energy / Heat Conserved (pool ball)
• Inelastic collision: Kinetic Energy / Heat not Conserved
  • perfectly inelastic collision: two objects stick together 

Open vs Closed

• Open system: Momentum changes
• Closed system: Momentum doesn’t change

5. Momentum

Momentum: How hard is it to stop something?

Momentum (kg * m/s)

$$P=mv$$

Collisions with conserved momentum:

$$p_{initial}=m_1{v}_1+m_2{v}_2$$ $$p_{final}=(m_1+m_2)v_{final}$$

Conservation of momentum (with no external force)

$$p_{initial}=p_{final}$$

Elastic collision: Heat / Kinetic energy is not generated

• Eg. knocking a billiard ball, and the cue ball stops
• $K_{bi}+K_{si}=K_{bf}+K_{sf}$

Inelastic collision: Heat / Kinetic energy is generated

• Might go into heat/sound/potential
• $K_{ai}+K_{bi}!=K_{af}+K_{bf}$
• Perfectly inelastic: Objects stick together and continue moving

Impulse: Change in momentum

$$Impulse(J)=F_{avg}\Delta t=m\Delta v$$

• Measured in Ns because $mat=mv$
• Is the area under a F-t graph

Impulse-Momentum Formula

$$\Delta p=F\Delta t$$

$Power=\frac{work}{time}$

2D and Elastic Collisions

Moving Mass

$$v_1^{\prime }=\frac{m_1-m_2}{m_1+m_2}{v}_1+\frac{2m_2}{m_1+m_1}{v}_2$$

Non-Moving Mass

$$v_2^{\prime }=\frac{2m_1}{m_1+m_2}{v}_1-\frac{m_1-m_2}{m_1+m_2}{v}_2$$

6. SHM

7. Torque and rotation

Torque

$$T=r\times f\times \sin \theta$$

Inertia

$$I=m{r}^2$$

Angular momentum:

$$L=lw$$

• L = angular momentum (kg m2 rad / s)
• I = moment of inertia (kg m2)
• w = angular velocity (rad / s)