Newton’s Laws of Motion Linear Kinetics

Aim The aim of these slides is to introduce Newton’s Laws of Motion These slides include an introduction to: Newton’s Law of Gravitation Newton’s 1st, 2nd and 3rd Laws of Motion The relationship between forces applied to bodies and the motion that those bodies experience

Newton’s Law of Gravitation All bodies are attracted to one another with a force which is proportional to the product of their masses (m), and inversely proportional to the square of the distance (d) between them

Implications of Newton’s Law of Gravitation Mass Greater mass = greater gravitational force Smaller mass = lower gravitational force Distance Greater distance = smaller gravitational force Smaller distance = greater gravitational force Most bodies in sport have relatively small mass Attractive force between them can be considered negligible

Weight rpoles requator r = radius of earth requator > rpoles Weight (W) is the attractive force between the earth and any body in contact with it or close to its surface Product of the mass (m) of the body and the acceleration caused by the attractive force between it and the earth (g = 9.81 m·s-2) i.e. W = m × g Gravity is based on: Mass of bodies Distance between bodies rpoles requator r = radius of earth requator > rpoles gequator < gpoles Wequator < Wpoles

Newton’s First Law of Motion Law of Inertia Every body will remain in a state of rest or constant motion (velocity) in a straight line unless acted on by an external force that changes that state A body cannot be made to change its speed or direction unless acted upon by a force(s) Difficult to prove on earth due to the presence of friction and air resistance

Examples of Newton’s First Law? Air Resistance Friction & Air Resistance

Newton’s Second Law of Motion Law of Acceleration A force (F) applied to a body causes an acceleration (a) of that body which has a magnitude proportional to the force, and takes place in the direction in which the force acts Vitally important in sport as it forms the link between force and motion: Force = mass × acceleration F = m × a

Applications of Newton’s 2nd Law Assuming mass remains constant, the greater the force the greater the acceleration Acceleration is inversely proportional to mass if force remains the same and mass is halved, then acceleration is doubled if force remains the same and mass is doubled, then acceleration is halved F = 500 N a = ? F = m × a  a = 333 m·s-2

Newton’s Third Law of Motion Law of Reaction For every force that is exerted by one body on a second body there is an equal (magnitude) and opposite (direction) simultaneous force exerted by the second body on the first Therefore every force which is applied by a body is accompanied by a reaction force on that body Difficult to visualise but can be felt: e.g. In boxing the force applied by a punch is experienced by the opponent’s chin and the puncher’s hand

Examples of Newton’s 3rd Law Ground Reaction Force (GRF) is a special type of force explained by Newton’s 3rd Law of Motion Equal in magnitude and opposite in direction to the force applied to the ground by the body Needs to be considered separately in horizontal (friction) and vertical (normal) directions

Explaining motion using Newton’s Laws - SVJ Weight (W) vector Vertical GRF (Fz ) vector C Fz (N) Time (s) A D B E B D E A C D

Effects of Forces If only one force acting: F = m × a If two (or more) forces acting: ∑F = m × a In SVJ: Fz - W = m × az 

Effect of Forces B D A C E Fz = W az = 0 Fz < W az = negative az = g Fz = W az = 0 Fz > W az = positive C Fz (N) Time (s) A D B E B D A C E

Explaining motion using Newton’s Laws - SVJ Weight (W) vector Vertical GRF (Fz ) vector Acceleration (m·s-2) Time (s) C A D B E E A B D C D

Summary Newton’s Law of Gravitation Newton’s First Law (Inertia) Attractive forces exist between bodies (e.g. a body and the Earth) that are proportional to the product of their masses and inversely proportional to the distance between them Newton’s First Law (Inertia) A force is required to accelerate (i.e. change the velocity of) a body Newton’s Second Law (Acceleration) The acceleration of a body is proportional to the sum of the forces acting on it Newton’s Third Law (Reaction) Any body that applies a force to another body experiences a simultaneous reaction force that is equal in magnitude and opposite in direction to the applied force

Recommended Reading Enoka, R.M. (2002). Neuromechanics of Human Movement (3rd edition). Champaign, IL.: Human Kinetics. Pages 57-59 & 64-66. Grimshaw, P., Lees, A., Fowler, N. & Burden, A. (2006). Sport and Exercise Biomechanics. New York: Taylor & Francis. Pages 69-80 & 97-101. Hamill, J. & Knutzen, K.M. (2003). Biomechanical Basis of Human Movement (2nd edition). Philadelphia: Lippincott Williams & Wilkins. Pages 341 & 351-356. McGinnis, P.M. (2005). Biomechanics of Sport and Exercise (2nd edition). Champaign, IL.: Human Kinetics. Pages 77-99.