Biomechanics cheat sheet PDF

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Biomechanics: The study of forces acting on and within! a living structure and the motion that results. Kinematics: the study of motion in terms of time and location, without any consideration for what causes the motion. Kinetics: the study of the action of forces that cause motion. Qualitative Biomechanics: verbal/ observational description of human movement. e.g. “his speed increased” Quantitative Biomechanics: numerical description of human movement. e.g. “his speed changed from 8m/s to 10m/s”. Seven si standards, 3 main ones; Length, mass & Time. Other 4 are: electric current, temperature, quantity of matter & luminous intensity. Scalar: Has Magnitude only. eg. travelled 10m = distance Vector: Has Magnitude and Direction is designated in bold.! eg. travelled 10m in a northerly direction = displacement. 3 components: 1: length = magnitude of vector. 2: direction = direction which vector acts. 3: starting point = point of application. Translation (linear motion): when a body moves but doesn’t rotate. When all points on a moving body move along paths of same distance. 2 types: rectilinear motion = straight lines e.g. train moving on straight tracks. curvilinear motion = curved/circular e.g. throwing stone at angle (no rot). Rotation (angular motion): Pure rotation is when a body rotates about a point or axis of rotation and this point/axis does not translate. When all points on the body move through the same angle in the same direction and the axis is stationary. e.g. pinwheel. General motion: when an object uses both angular and linear motion together. The object rotates around a translating axis. e.g. ball being thrown with backspin. Position; a location point with respect to a reference point or origin. Distance: Complete path of travel; Scalar; m Displacement: Change in position; Vector Average Speed: v=∆s/∆t speed=distance/time. Line above letter means its average/mean. Scalar. Known as the first derivative of distance. Average Velocity: v =∆s/∆t velocity = displacement/time. Vector. The definitive, general way to calculate average velocity is: v=(x2 - x1)/(t2 - t1) Where (in one-dimension):! x2 is the final position or final x-coordinate; x1 is the initial position or initial x-coordinate; t2 is the final time (when x2 is reached);! t1 is the initial time (when x1 is reached). ALSO: v= ∆x / ∆t Where (in a one-dimensional sense): ∆x is the change in displacement; ∆t is the change in time. Average/ instantaneous velocity: In a displacement/time graph a constant velocity motion will show a straight line. Average/ instantaneous Velocity: In a displacement-time graph, a constant velocity motion will show a straight line. The average velocity is the slope of the straight line. v = ∆x / ∆t =(xF –x0)/(tF –t0) Where xF is the final displacement (100m) at tF (10s) and x0 is the initial displacement (0m) at t0 (0s). Acceleration: the change in velocity per unit of time in a given direction. (don’t confuse w/ velocity, which is the change in displacement, per unit of time in a given direction) Velocity measures how fast position changes; Acceleration measures how fast velocity changes! ā =∆v / ∆t =(v2 –v1)/(t2 –t1) e.g. A 100m sprinter has a velocity of 3m/s at 10m and a velocity of 8m/s at 20m. If it took 2s to get from 10m to 20m, what was the sprinter's acceleration? ā = (vfinal – vinitial) / ∆t =(8–3)/2 (m/s/s) =5/2! = 2.5 m/s2 Negative acceleration > Speeding up in a positive direction. Slowing down in a negative direction. Jerk: rate of change of acceleration: = ∆a / ∆t Angular motion: Exactly the same principles apply to angular motion as in linear motion “”v = omega.r””omega () = angular velocity in rad/s (/s)(One radian is 180/π degrees, or ~ 57.3° (1rad = 57.3°)); r = radius (m);v = linear velocity if released (m/s). 2D motion: Also known as planar motion. Sports in single plane; long jump, cycling etc. suffices x&y indicate vertical & horizontal. 3D motion: most in 3d. x,y,z all at right angles. Motion with constant acceleration; linear motion with constant acceleration, uniformly increases in velocity e.g, free falls & projectiles. At initial time, t = 0, initial velocity = v1. The object moves with a constant acceleration, a. After time t, the object moves a displacement, ∆s, and the final velocity, v2, will be:v2= v1+ a.t NB. This is often written as:v= u+ a.t… Equations of motion for constant acceleration: “v = u + a.t” “v2= u2+

2.a.s” “s = u.t + ½.a.t2” (v = final velocity (v2) u = initial velocity (v1) a = constant acceleration(a) s = displacement (∆s)t = time (∆t)) “v2= v1+ a.∆t” “v22= v12+ 2.a.∆s” “∆s= v1.∆t + ½.a.∆t2” (v2= final velocity (v)v1= initial velocity (u)a= constant acceleration(a)∆s= displacement (s)∆t = time (t)) “v2= v1+ a.t” “v22= v12+ 2.a.s” “s= v1.t + ½.a.t2” (v2= final velocity (v)v1= initial velocity (u)a= constant acceleration (a)s= displacement (∆s)t = time (∆t)) e.g. An airplane accelerates on a runway to take-off. If it has a constant acceleration, a, 2.5m/s2, how long must the runway be if the airplane’s take-off velocity must be>71m/ s? v, u & a are known, find s ... which equation has v, u, a and s? v2= u2+ 2.a.s 712= 0 + 2*2.5*s s = 712/ (2*2.5) = 1008.2m s = 1008.2m Assuming no air resistance, the VERTICAL motion of any freely flying or falling body can be described using the three equations presented earlier ... noting:Acceleration, a, becomes g(g = -9.8m/s2) Inertia: is the property of an object that tends to resist any change to the state of motion. E.g. Car suddenly stops and passengers are thrown forward coz they have inertia. The inertia of a body is the reluctance of that body to move or to change its state of motion. mass, is the measure of an objects inertia in kg. i.e. bigger mass, bigger inertia. weight: force of attraction the earth exerts on an object. (Don’t confuse with mass which is the quantity of matter. momentum: mass x velocity. Vector. SI unit: p= m.v = kg x m/s = kg.m/s force: something that causes or tends to cause a body to change its state of motion or rest. Vector. F = m x a. SI unit: Newton (N). 1N is defined as the force required to accelerate a mass of 1kg by 1m/s2. When more than one force works on an object, you have to consider them all, for the net effect of all the forces. The net or resultant force can be determined by vector addition (tail-to-head method) found by drawing arrow from tail of 1st vector to head of last; gives the direction and magnitude of the resultant force. Newtons first law of motion “A body remains at rest or in motion with a constant momentum unless a force is applied on it.” E.g rugby scrum; net force is 0, no movement. Projectile: air resistance, gravity. Internal & External forces: Internal is within a system e.g. muscle forces, ligament forces, reaction forces. External: acting on system from outside e.g. gravity, push in back, buoyancy. inertial frame of reference: any coordinate/axis system that is at rest or moving with constant velocity. e.g. Earth; its surface can be said to be moving at a constant velocity. centric; has the line of action that passes through the bodys axis of rotation. results in linear motion. eccentric forces; has a line of action that does not pass through the body’s axis of rotation. results in angular or general motion. torque: vector; the angular equivalent of force. the influence on one body by another body inclining it to change it’s state of angular motion. T = F x d (in N.m) Newtons 3 laws of linear and angular motion first linear is above angular is same but change to “constant angular momentum” Angular momentum (H) = moment of inertia (I; the angular equivalent of mass) x angular velocity (w) Newton’s Second Law of Linear/ Angular Motion: F= m.a (Linear) T (torque) = I (moment of inertia) x a (angular acceleration) (Angular) “Linear/ Angular acceleration is always in the same direction as the net external force/torque that causes that acceleration.” Third Law: When one object exerts a force/torque on a second object, the second object exerts a force/ torque of equal magnitude on the first object, but in the opposite direction free body diagrams b) Net external force = 200 + 200 – 300! = 100N! c) a = F/m = 100/1000! = 0.1m/s2! 2nd law - impulse-momentum theory! conservation of momentum: the momentum of a system is the sum of the momenta of all objects that make up the system. Law states that if there is no external force; the momentum doesn’t change. F.∆t =∆p ie.ifF=0then∆p=0Or p initial= p final angular momentum; reluctance to be accelerated (angularly), positively or negatively, about an axis of rotation. moment of inertia; Two things define; 1. Mass - Consider closing wood door or iron door. 2. Distribution of mass (radius of gyration, k.) the further that the body’s mass is distributed away from a given location of the axis of rotation, the greater the body’s moment of inertia about that axis. (greater k = greater I) diving, ice skating.

gravitation - attraction force (pulling) that exists between two objects that have mass. three laws; 1. greater the masses of one or both bodies, the greater the gravitational force i.e. sumo & earth vs. jockey & earth (which has greater weight?) 2. the smaller the distance between the two bodies, the greater the gravitational force. 3. The gravitational attraction force between most objects is miniscule. i.e. between two people (90kg) if they're 1m apart. F = 6.67x10-11 x 90 x 90 / 12 = 5.4 x10-7N! centre of mass- A body’s CM is the point about which the net torque, produced by all the body’s individual mass particle weight forces, equals zero. The centre force where the weight force is deemed to act. Interchangeable with centre of gravity. is not a real point. normal forces and friction - normal means “perpendicular to” i.e flat ground/ slope etc. It is a contact force thus it only exists when it is in contact with the ground/table (different to gravitational forces where no contact is required.) friction force prevent or resist two objects from sliding across each other. Nothing is ever really flat, jagged edges work against each other keeping it in place. 3 types of friction; static (no movement, shoe and court), sliding (less than static, this is why its easier to keep a heavy object moving once it’s started) & rolling (retarding force during rolling, much smaller than other 2.) Impulse = f x H $

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= momentum! = mass x velocity! = m.v! net impulse = (delta the triangle symbol which means change in) (m.v)! Work - when a force is exerted on an object making it move a distance! = force x distance moved. (N x deltad)! It is a scalar quality and is measured in joules (J)! Look at more complex example Power - efficiency of work transfer. (p) watts (W) = work / change in time. Second formula which is F x v (v is delta d / delta t)! Energy - 1j of work is done when 1n of force moves an object 1m! W = F.delta d! 1= 1.1! More energy is used going against gravity.! total energy = ke + pe! 2 types -! Potential - Stored energy ready to release (trampoline)! Potential - Due to gravity or due to objects that can be stretched, bent, squeezed. (trampoline, elastic band & bouncy ball) PE = m x g x h e.g. mass = 60kg height= 3m gravity = 9.8m/s2 (No need for negative sign because energy is scalar and we don’t need the direction.) In joules (J)Kinetic - Velocity Kinetic - KE = 1/2 x m x v2! = half x mass x velocity squared. v2 = u2 + 2.a.s (a being 9.8, and s being the height) In Joules (J) Work- Energy Theorem. Work/Energy are essentially the same things. Net work done (W) on an object equals the change in kinetic energy.

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