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 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 is the approach to solve problems involving conservation of momentum in two dimensions?

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

  
• What is the equation for total momentum before and after a collision along the x-axis?

  m1 v1x + m2 v2x = m1' v1x' + m2' v2x'
• What happens to the momentum equation when ball 2 is initially at rest?


  The equation simplifies to m1 v1x = m1' v1x' + m2' v2x' with v2x = 0.
• How do you resolve final velocities into components along the x and y-axis?


  By using trigonometry based on the angles given in the diagram.
• What is the equation for total momentum before and after a collision along the y-axis?

  m1 v1y + m2 v2y = m1' v1y' + m2' v2y'
• What does the equation 0 = m1' v1y' + m2' v2y' imply when ball 2 is initially at rest?

  It implies that the initial momentum in the y-direction is zero.
• What is the significance of the angles in the equations derived for momentum conservation?

  The angles are used to resolve the final velocities into their components along the axes.
• What are the two types of collisions?

  Elastic and inelastic collisions.
• What is conserved in an elastic collision?


  Both momentum and kinetic energy are conserved.
• What happens in an inelastic collision?


  Only momentum is conserved, while some kinetic energy is converted into other forms.
• What is the formula for kinetic energy of a non-relativistic particle?


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


  By rearranging the momentum formula to express velocity and substituting it into the kinetic energy formula.
• What is centripetal acceleration?

  Centripetal acceleration is experienced by objects moving in a circular path.
• How is centripetal acceleration derived?


  It is derived using vector diagrams and the relationship between linear speed and radius.
• What is the formula for centripetal force?


  F = $\frac{mv^2}{r}$
• What is the direction of centripetal force in circular motion?

  Centripetal force always acts towards the center of the circle.
• What is angular velocity?

  Angular velocity (ω) is the angle an object moves through per unit time.
• How can angular velocity be calculated?


  Angular velocity can be calculated by dividing linear velocity by the radius of the circular path.
• What is the relationship between angular velocity and time period?

  Angular velocity can be found by dividing the angle in a circle in radians by the object's time period.
• What is the formula for centripetal acceleration in terms of angular velocity?


  a = rω²
• What is the relationship between linear speed and angular velocity?


  Linear speed is equal to the radius times the angular velocity: v = rω.
• What is the significance of centripetal force in circular motion?


  Centripetal force is required to produce and maintain circular motion.
• How does centripetal force relate to Newton's second law?

  Centripetal force can be derived from Newton's second law, F = ma, where a is centripetal acceleration.