1. Roll and Fall Playing with the Laws of Motion Games Fundamentals © by Jarek Francik Kingston University, London 2007 - 2013

2. Agenda Laws of Motion Inclined Plane Friction Falling and Throwing Demo

3. Newton’s Laws of Motion

4. 1.If no external force acts on a particle, or all the forces are balanced, then the particle moves without any change in velocity if it was in restif it was in motion it stays at restit stays in motion NEWTON’S LAWS OF MOTION

5. Notice that the behaviour of objects around us is usually affected by air resistance and friction NEWTON’S LAWS OF MOTION

6. 2.If unbalanced external net force acts upon an object then the object moves with the acceleration directly proportional to the magnitude of this force and in the same direction and inversely proportional to the mass of that object NEWTON’S LAWS OF MOTION

7. The phenomenon of falling is ruled by the Newton’s second law. The force acting is the gravitational force The acceration is on the surface of Earth always the same: g = 9.81 m/s 2 F g = mg NEWTON’S LAWS OF MOTION

8. Notice that the behaviour of objects around us is usually affected by air resistance and friction NEWTON’S LAWS OF MOTION

9. 3.Whenever A exerts a force on B, B simultaneously exerts a force on A with the same magnitude and opposite direction NEWTON’S LAWS OF MOTION

10. Friction Force

11. INCLINED PLANE  F g = mg

12. INCLINED PLANE  F g = mg mg sin  mg cos 

13. INCLINED PLANE  F g = mg mg sin  mg cos  F N = mg cos 

14. INCLINED PLANE  F g = mg F = mg sin  F N = mg cos  F = F g + F N

15. INCLINED PLANE  F N = mg cos 

16. INCLINED PLANE  F g = mg F = mg sin  F N = mg cos  F F = fmg cos 

17. INCLINED PLANE 

18.  V VhVh VvVv

19.  V h = V cos  V v = 0

20.  INCLINED PLANE V h V cos  V v = 0

21. Friction Force

22. FRICTION FORCE F F = f 1 mgF V F F F = f 2 mg V F F = 0 V = 0

23. Falling & Throwing

24. FALL & THROW V mg V uniform velocity F = mg gravitational force PARABOLIC TRAJECTORY

25. FALL & THROW V VhVh V V h = V cos  V V = V sin  + at

26. FALL & THROW If there is no initial horizontal component V h = 0 trajectory is linear Non-zero horizontal component V h ≠ 0 trajectory is parabolic Both horizontal and vertical components are non zero V h ≠ 0 V V ≠ 0 trajectory is also parabolic What if V V < 0 yes, trajectory is also parabolic

27. Demo

28. Accelerated Motion double v = m_sprite.GetSpeed(); v += 10; m_sprite.SetSpeed(v);... // code above – before Update! m_sprite.Update(GetTime()); or: m_sprite.SetSpeed(m_sprite.GetSpeed() + 10); DEMO

29. Free Fall double vx = m_sprite.GetXVelocity(); double vy = m_sprite.GetYVelocity(); vy -= 10; m_sprite.SetVelocity(vx, vy); or: m_sprite.SetVelocity(m_sprite.GetXVelocity(), m_sprite.GetYVelocity()-10); DEMO

30. Bounce if (m_ball.GetBottom() >= 600 && m_ball.GetYVelocity() < 0) m_ball.SetVelocity(m_ball.GetXVelocity(), -0.8 * m_ball.GetYVelocity()); DEMO