Further Mechanics

• What does Newton's 2nd law state?


  F = ma
• What does the equation $F =$$\frac{\Delta p}{\Delta t}$ represent?


  It represents the relationship between force, change in momentum, and impact time.
• What is impulse defined as?

  Impulse is defined as the change in momentum.
• If a ball is hit with a force of 100 N for an impact time of 0.5 s, what is the change in momentum?

  The change in momentum is 50 kgm/s.
• When is momentum conserved in an interaction?

  Momentum is conserved when no external forces act on the system.
• How can momentum be conserved differently in two dimensions?

  Momentum can be conserved along different dimensions by resolving motion into components along perpendicular axes.
• What are the steps to solve problems involving conservation of momentum in two dimensions?

  • Resolve the motion into components along perpendicular axes (e.g., x and y-axis).
  • Solve the resultant pair of problems in one dimension simultaneously.

  
• What are the two types of collisions?

  The two types of collisions are elastic and inelastic collisions.
• What is an elastic collision?

  An elastic collision is one where both momentum and kinetic energy are conserved.
• What happens in an inelastic collision?


  In an inelastic collision, only momentum is conserved, and some kinetic energy is converted into other forms.
• What is the formula for kinetic energy of a non-relativistic particle?


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


  By rearranging the momentum formula $p =$$mv$ to $v =$$\frac{p}{m}$ and substituting into $E_k =$$\frac{1}{2}mv^2$.
• What is angular displacement?


  Angular displacement is the angle turned through by an object in any given direction, measured in radians or degrees.
• How is angular velocity defined?


  Angular velocity is the angle an object moves through per unit time.
• What is the formula for angular velocity?


  The formula is $\omega =$$\frac{v}{r}$.
• How can angular velocity be calculated using the time period?


  Angular velocity can be calculated using $\omega =$$\frac{2\pi}{T}$.
• What is centripetal acceleration?

  Centripetal acceleration is the acceleration experienced by objects moving in a circular path.
• Why does an object moving in a circular path experience centripetal acceleration?


  Because its velocity is constantly changing in direction, even if its speed is constant.
• What is the relationship between centripetal force and circular motion?


  Centripetal force is required to produce and maintain circular motion, acting towards the center of the circle.
• What is the formula for centripetal force?


  The formula is $F =$$\frac{mv^2}{r}$.
• How can centripetal force be expressed in terms of angular velocity?


  Centripetal force can be expressed as $F =$$mr\omega^2$.