The Laws of Motion

1. The Laws of Motion …or, Newtonian mechanics PHY 101 Week2

2. Newton’s Laws of Motion • The law of inertia. An object in motion remains in motion with constant velocity if the net force on the object is 0. • Force and acceleration. If the net force acting on an object of mass m is F, then the acceleration of the object is a = F/m. Or, F = ma. • Action and reaction. For every action there is an equal but opposite reaction. PHY 101 Week2

3. Newton’s second law PHY 101 Week2

4. Newton’s second law of motion F = m a • F = force acting on the moving object, a vector • m = mass of the moving object • a = acceleration of the moving object, a vector What is “force?” What is “mass?” If the force is known, Newton’s second law states how the object (on which the force is acting) accelerates: PHY 101 Week2

5. Force and acceleration are vectors. A vector has both magnitude and direction. PHY 101 Week2

6. Three kinds of acceleration m speeds up m slows down m changes direction PHY 101 Week2

7. UNIFORM CIRCULAR MOTION PHY 101 Week2

8. Example Centripetal acceleration (Christian Huygens ,1673) Therefore, the force on m is The “string tension” is the strength of the force exerted by the string at either end. PHY 101 Week2

9. Analyze free fall including air friction The aerodynamic drag force (C) depends on the size, shape and surface roughness; it is about the same for both balls. • The gravitational acceleration (g) is independent of mass. • Effect of air is inversely proportional to mass: • heavy --- small effect of air • light --- large effect of air PHY 101 Week2

10. Newton’s third law PHY 101 Week2

11. Which vehicle exerts a greater force ― the tow truck or the car? PHY 101 Week2

12. Action means force. Newton’s laws of motion • The law of inertia. An object in motion remains in motion with constant velocity if the net force on the object is 0. • Force and acceleration. If the net force acting on an object of mass m is F, then the acceleration of the object is a = F/m. Or, F = ma. • Action and reaction. For every action there is an equal but opposite reaction. PHY 101 Week2

13. force on B due to A force on A due to B For every action there is an equal but opposite reaction. Newton’s third law Whenever one object exerts a force on another object, the second object exerts an equal but opposite force on the first object. Forces always occur like this, in pairs. We will see than this is very hard to accept! It is just not common sense. That is why it took a great genius like Newton to figure it out. PHY 101 Week2

14. Example – A collision PHY 101 Week2

15. Universal Gravitation --- an example of Newton’s third law PHY 101 Week2

16. The Earth pulls the apple down (“action”). The apple pulls the Earth up (“reaction”). The two forces are equal (but opposite). PHY 101 Week2

17. When does a scientific theory become an accepted fact? PHY 101 Week2

18. A puzzle: The truck pulls to the right. According to Newton’s third law, the car pulls to the left with an equal force. So how can they start moving, or accelerate? Resolution: Consider each part separately, and don’t forget that other forces are also acting. PHY 101 Week2

19. Harold Edgerton’s high speed photograph of Wes Kessler kicking a football. The force exerted by the ball on the toe (reaction) is equal to the force exerted by the toe on the ball. Really hard to accept! PHY 101 Week2

20. Momentum, p = mv Total momentum is conserved: Proof PHY 101 Week2

21. unified by Maxwell’s theory comes from QCD, the interaction of quarks and gluons not really a force, but an interaction that causes certain radioactive decays The four fundamental forces • Gravity • Electromagnetic • Strong nuclear force • Weak nuclear force PHY 101 Week2

22. FIN PHY 101 Week2

23. differential equation Newton’s second law and calculus Isaac Newton invented calculus to solve the equation of motion – to calculate motion for the force that is acting. Generally, calculus is the mathematics that describes continuous change. PHY 101 Week2