What is biomechanics?
The mechanics of the structures and movements of living
organisms.
What is mechanics?
The branch of applied mathematics that deals with the motion and equilibrium of bodies and the action of forces.
What are the main themes of biomechanics?
 Safety: Protection from injury
 Effectiveness: Maximization of the output/performance
 Efficiency: Economy of energy expenditure
What are some special challenges faced by biomechanists?
 Humans cannot be measured or tested in the same way that machines can. {Mr. Krabs vs Robot Krabs}
 "Design objectives" for human bodies are not always clear
 Human bodies are different from one another
What is statics?
 Branche of mechanics dealing with systems in the constant state of motion
 Study of systems that are at rest or are moving at constant velocity
What is dynamics?
 Branch of mechanics dealing with systems subject to acceleration.
 Study of systems in which accelerations are present.
What is kinematics? List examples of kinematic variables.
 Study of the description of motion.
 Examples
 Position
 Velocity
 Displacement
 Speed
 Distance
 Acceleration
 Position
 Velocity
 Displacement
 Speed
 Distance
 Acceleration
What is kinetics? List some examples.
 Study of action of forces (explanation of motion)
 Examples
 Force
 Moment (torque)
 Inertia
 Impulse
 Force
 Moment (torque)
 Inertia
 Impulse
What is the difference between a vector and a scalar?
 Vector
 Two components: Magnitude and direction (+ or )
 Examples
 velocity
 displacement
 force
 acceleration
 Scaler
 Directionless quantities. only magnitude is relevant
 Examples
 Mass
 Speed
 Distance
 Time
 Two components: Magnitude and direction (+ or )
 Examples
 velocity
 displacement
 force
 acceleration
 Directionless quantities. only magnitude is relevant
 Examples
 Mass
 Speed
 Distance
 Time
How do you compute displacement?
X_{2}X_{1}
A vector change in position.
How do you compute Distance?
 a scalar change in position
 how far you traveled regardless of direction.
symbols of position, distance, displacement, speed, velocity, and acceleration in linear and angular motion.
What are the 3 properties of force?
Magnitude, Direction, and point of application.
Why do biomechanists assume that body segments are rigid?
 Rigid body: made up of particles whose distances from one another are fixed. No deformation
 Body segments (e.g., thigh, trunk, forearm) commonly assumed to be rigid bodies.
 Assumption not true in many cases
 Assumption great simplifies the mathematics of biomechanical modeling.
What is Newton's 1st Law in a linear form?
 aka Law of Inertia
 "Bodies remain at rest or in uniform motion (constant velocity) until acted upon by unbalanced forces."
 Bodies at rest or in uniform motion are said to be in equilibrium.
 Forces acting on bodies in equilibrium are completely balanced (net force is zero)
 Every body continues in its state of rest or motion in a straight line unless compelled to change that state by external forces exerted upon it.
What is Newton's 2nd Law in a linear?
 Also called Law of Acceleration.
 “Net force applied to a body is proportional to the resulting acceleration.”
 Constant of proportionality is a scalar property of the body called mass: F = ma
 Net force and acceleration are vectors pointing in the same direction.
 “Net” force: S F = ma
What is Newton’s 3^{rd} Law in a linear form?
 a.k.a. Law of Reaction.
 “For every action, there is an equal and opposite reaction.”
 In the case of two bodies in contact, the force exerted by the first on the second is equal and opposite to the force exerted by the second on the first.
What is a whiplash injury and what is its connection to Newton's Law?
 Hit from behind, but head snaps backward?
 No force acts to move the head forward with rest of body and car.
 Head stays in place (1st Law), neck extends.
 Followed by flexion phase  head moves forward while body is stationary
My words  "The body is attached the car via the seat belt and the head is not, thus there is no force stopping the head from continuing with its forward momentum established by the moving car."
How to calculate a net force when multiple forces are acting on an object?
 The net force is the vector sum of all forces action in the system
Differences between mass and weight?
Mass:
 Quantity of matter composing a body
 Scalar
 no mass = no mechanical identity
 symbol: m
 standard unit: kg (kilogram)
Weight:
 Weight: gravitational force exerted on an object by the earth. E.g. earth & moon
 F = ma ===> W = mg
 g is always a downward acceleration, so W is always a downward force.
 Weight is a force and has the same units.
How to find the center of mass of an object in threedimensions?
 Center of mass (COM): Point about which the sum of moments of a body's weight is zero
 a point around which the mass of a body is balanced in all directions
 3dimensional balancing point
What are internal and external forces and how are they defined in biomechanics?
 Internal forces are forces that are internal to the system and external forces are the forces which are external to the system.
 The classification of internal and external forces are used for convenience.
 Internal or external can be changed depending on the scope of the system.
What is ground reaction force?
 Commonly measured force in biomechanics.
 GRF: Force exerted by floor on feet.
 Equal and opposite to force exerted by feet on floor (3rd Law).
 Standing GRF = 1 body weight (BW).
What is an inflection point?
 “point of inflection” where slope of displacement vs time curve switches from increasing to decreasing
 Acceleration sign changes at an inflection point
How to resolve a vector to its components using sine and cosine?
 “Resolve”: to break a vector into its 2D or 3D components
 Given: Magnitude and angle
 Find: x and ycomponents of vector in 2D
 cos q = Vx / V, sin q = Vy / V
 Vx = V cos q , Vy = V sin q
How to add vector components?
 “Resultant”: Sum of vectors
 Given: magnitudes of vector components or multiple vectors.
 Find: Magnitude and direction of resultant.
 Vx2 + Vy2 = V2, tan q = Vy / Vx
e. V = (Vx2 + Vy2)½, q = tan1 (Vy / Vx)
How to add multiple vectors?
 Add by placing vectors headtotail.
 Find: Magnitude and direction of resultant.
 Vx2 + Vy2 = V2, tan q = Vy / Vx
 V = (Vx2 + Vy2)½, q = tan1 (Vy / Vx)
What is each variable in constant acceleration equations?
 v = vo + a t
 x = xo + vo t + ½ a t^{2}
 v^{2}  vo^{2} = 2 a (x  xo)
 v: velocity at time t, vo: initial velocity, a: acceleration at time t, t: time, x: position at time t, xo: initial position,
 v = vo + a t
The only force acting on a projectile?
Gravitational force
How to solve a question of ‘How long does it take to …?’ under a constant acceleration?
 Solve one of the following equation for time t
 x = xo + vo t + ½ a t^{2}
 t = (v  vo) / a
How to solve a question of ‘How far will the object travel …?’ under a constant acceleration?
 Solve one of the following equation for position x
 x = xo + vo t + ½ a t^{2}
 v^{2}  vo^{2} = 2 a (x  xo)
How to solve a question of ‘What is the velocity of the object …?’ under a constant acceleration?
 Solve one of the following equation for velocity v
 v = vo + a t
 v^{2}  vo^{2} = 2 a (x  xo)
How to solve a question of ‘What is the acceleration of the object …?’ under a constant acceleration?
 Solve one of the following equation for acceleration a
 x = xo + vo t + ½ a t^{2}
 v^{2}  vo^{2} = 2 a (x  xo)
 v = vo + a t
What is optimal angle of release?
 Angle of release for the maximum length of a projectile travel
 Depends on the vertical position of release and the vertical position of landing
 45º
How to calculate torque?
 Forces cause translations
 Moments (a.k.a. “torques”) cause rotations
 Moments caused by a force acting at a distance from an axis of rotation: M = F · d
 Units of moment are force times distance, N m, or “newtonmeters”
Examples of the first, second and third class levers in a human body?
 First: neck joint
 Second: ankle joint for plantar flexion
 Third: elbow joint for flexion
Which class levers are the most common in a human body?
Third class levers
What is Newton’s 1st, 2nd, and 3rd Law in their angular forms?
 First: q = qo + ωo t + ½ a t^{2}
 Second: ω = ωo + a t
 Third: ω^{2}  ωo^{2} = 2 a (q  qo)
 First: q = qo + ωo t + ½ a t^{2}
 Second: ω = ωo + a t
 Third: ω^{2}  ωo^{2} = 2 a (q  qo)
How to calculate a muscle force during a static action?
 Create a “free body diagram”
 Shows only body of interest and forces applied to it
 Use ∑F = 0 and/or ∑M = 0
What is the ‘forcevelocity tradeoff’?
 Most of the lever systems in a human body have inefficiency in muscle force use
 However, the systems have an advantage of velocity at the endpoint
What is moment of inertia?

Moment of inertia (I) is to angular motion what mass is to linear motion.
 Moment of inertia depends on the mass and its distribution.
How to calculate moment of inertia.
In layman's terms, what does the moment of inertia measure?
How hard is it to rotate a body.
 Why do trackandfields sprinters bend their knee joints during 100m dash?
 To decrease moment of inertia
 Moment of inertia for the human body can be changed
 Gymnastics and diving –
 Moment of inertia for twisting is smaller/larger than moment of inertia for somersaulting.
 Figure Skating
 Spinning with arms outstretched is slower/faster than spinning with arms held tight to body
 Running/walking/marching
 Easier/harder to rotate leg at hip with knee bent than with knee straight
What is momentum?
 Momentum
 amount of motion
 mass multiplied by velocity (P = m·v)
 2nd Law gives:
 amount of motion
 mass multiplied by velocity (P = m·v)
i. F = m a = m (v_{2}  v_{1}) / (t_{2}  t_{1})
ii. F = (m v_{2}  m v_{1}) / (t_{2}  t_{1})
 With no force applied, rate change of momentum is zero: Momentum is conserved. i. 0 = (m v_{2}  m v_{1}) / (t_{2}  t_{1})
ii. m v_{2} = m v_{1}
How to calculate momentum?
 P = m·v
 important in giving & receiving impact, collision, etc.
 vector
 unit: kg·m/s
What is impulse? How do you calculate impulse?
 The accumulated effect of force exertion over a period of time
 Change in momentum
 J = F·t
 J = DeltaP, which can be proven to equal the above equation by multiplying it by t/t
 How do figure skaters control their angular velocity about a vertical axis during spinning given that the angular momentum is constant?
 Angular momentum H = I ω

With no moment applied, angular momentum is conserved: I_{1} ω_{1} = I_{2} ω_{2}
 Angular velocity can be changed by changing moment of inertia.
 when I increases, ω must decrease
 when I decreases, ω must increase
What is the coefficient of restitution for two colliding objects?
What is the Coefficient of Restitution for a bouncing object?
What are the formulas for mechanical power?
What are the formulas for Mechanical Energy?
Conservation of ME: If the gravity is the only external force acting on a system, ME remains constant.
Explain the parallel axis theorem.
What are the rules for drawing a free body diagram?
What are centrifugal, and centripetal forces?
A fictional force.
Define moment arm.
the perpendicular distance from rotation axis to the line of action of the force.
 Muscle's moment arm: indication of the muscle's mechanical advantage at a joint.
 Moment arm depends on the muscle's line of action relative to the joint center
 Moment arm varies with joint angle.
What are the methods for calculating COM?
 Suspension Method
 Board and Scale Method
 Segmentation Method
Explain Mechanical Advantage.
Moments vs Moment arms