Further Mechanics

• What does Newton's 2nd law state?

  F = ma
• What does the equation $F =$$\Delta t \Delta(mv)$ represent?


  It relates force to momentum change over time
• How can you rearrange the equation $F =$$\Delta t \Delta(mv)$?


  $F \Delta t =$$\Delta p$
• What is impulse defined as?

  Impulse is the change in momentum
• If a ball is hit with a force of 100 N for 0.5 s, what is the change in momentum?

  50 kgm/s
• When is momentum conserved in interactions?

  When no external forces act
• How should you resolve motion in two dimensions for momentum conservation?

  Into components along perpendicular axes
• What is the equation for total momentum before a collision?

  Total momentum before = Total momentum after
• What happens to ball 2's velocity if it is initially at rest?

  Its initial velocity is zero
• How do you express the momentum equation for ball 1 moving in the x-direction?

  $m_1 v_{1x} =$$m_1' v_{1x}' +$$m_2' v_{2x}'$
• What is the significance of resolving final velocities into components?

  It helps solve for unknown values
• What is the formula for kinetic energy of a non-relativistic particle?

  $E_k =$$\frac{p^2}{2m}$
• How do you derive the kinetic energy formula from momentum?

  Substitute $v =$$\frac{p}{m}$ into $E_k =$$\frac{1}{2}mv^2$
• What is one radian defined as?

  Angle where arc length equals radius

  
• How do you convert degrees to radians?

  Multiply by $\frac{\pi}{180}$
• What is the formula for angular velocity?

  $\omega =$$\frac{v}{r}$
• How can angular velocity also be expressed in terms of time period?

  $\omega =$$\frac{2\pi}{T}$
• What is centripetal acceleration?

  Acceleration towards the center in circular motion
• Why must an object moving in a circle experience a centripetal force?

  To maintain circular motion
• What is the formula for centripetal force?

  $F =$$\frac{mv^2}{r}$
• How does centripetal force relate to Newton's second law?

  It is derived from $F =$$ma$
• What are the types of collisions?

  • Elastic: Both momentum and kinetic energy conserved
  • Inelastic: Only momentum conserved, kinetic energy converted
  • Explosions: Kinetic energy after is greater than before

  
• What are the steps to derive centripetal acceleration?

  1. Consider object moving at speed $v</text{ in a circular path of radius } r$
  2. Use similar triangles formed by velocity vectors
  3. Rearrange to find $\Delta v$ and then $a =$$\frac{v^2}{r}$
• What is the relationship between linear speed and angular velocity?

  • Linear speed $v</text{ is related to angular velocity } \omega$
  • $v =$$r\omega$
• What is the significance of centripetal force?

  • Required for circular motion
  • Always directed towards the center
  • Derived from Newton's second law