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What is biomechanics?

The mechanics of the structures and movements of living

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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?

  1. Safety: Protection from injury
  2. Effectiveness: Maximization of the output/performance
  3. 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


What is kinetics? List some examples.

  • Study of action of forces (explanation of motion)
  • Examples
    • 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


How do you compute displacement?


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.

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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?

  1. aka Law of Inertia
  2. "Bodies remain at rest or in uniform motion (constant velocity) until acted upon by unbalanced forces."
  3. Bodies at rest or in uniform motion are said to be in equilibrium.
  4. Forces acting on bodies in equilibrium are completely balanced (net force is zero)
  5. 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?

  1. Also called Law of Acceleration.
  2. “Net force applied to a body is proportional to the resulting acceleration.”
  3. Constant of proportionality is a scalar property of the body called mass: F = ma
  4. Net force and acceleration are vectors pointing in the same direction.
  5. “Net” force: S F = ma


What is Newton’s 3rd Law in a linear form?

  1. a.k.a. Law of Reaction.
  2. “For every action, there is an equal and opposite reaction.”
  3. 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?

  1. Hit from behind, but head snaps backward?
  2. No force acts to move the head forward with rest of body and car.
  3. Head stays in place (1st Law), neck extends.
  4. 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?

  1. The net force is the vector sum of all forces action in the system

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Differences between mass and weight?


  1. Quantity of matter composing a body
  2. Scalar
  3. no mass = no mechanical identity
  4. symbol: m
  5. standard unit: kg (kilogram)


  1. Weight: gravitational force exerted on an object by the earth. E.g. earth & moon
  2. F = ma ===> W = mg
  3. g is always a downward acceleration, so W is always a downward force.
  4. Weight is a force and has the same units.


How to find the center of mass of an object in three-dimensions?

  1. Center of mass (COM): Point about which the sum of moments of a body's weight is zero
  2. a point around which the mass of a body is balanced in all directions
  3. 3-dimensional balancing point


What are internal and external forces and how are they defined in biomechanics?

  1. Internal forces are forces that are internal to the system and external forces are the forces which are external to the system.
  2. The classification of internal and external forces are used for convenience.
  3. Internal or external can be changed depending on the scope of the system.


What is ground reaction force?

  1. Commonly measured force in biomechanics.
  2. GRF: Force exerted by floor on feet.
  3. Equal and opposite to force exerted by feet on floor (3rd Law).
  4. Standing GRF = 1 body weight (BW).


What is an inflection point?

  1. “point of inflection” where slope of displacement vs time curve switches from increasing to decreasing
  2. Acceleration sign changes at an inflection point

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How to resolve a vector to its components using sine and cosine?

  1. “Resolve”: to break a vector into its 2D or 3D components
  2. Given: Magnitude and angle
  3. Find: x- and y-components of vector in 2D
  4. cos q = Vx / V, sin q = Vy / V
  5. Vx = V cos q , Vy = V sin q


How to add vector components?

  1. “Resultant”: Sum of vectors
  2. Given: magnitudes of vector components or multiple vectors.
  3. Find: Magnitude and direction of resultant.
  4. Vx2 + Vy2 = V2, tan q = Vy / Vx

e. V = (Vx2 + Vy2)½, q = tan-1 (Vy / Vx)


How to add multiple vectors?

  1. Add by placing vectors head-to-tail.
  2. Find: Magnitude and direction of resultant.
  3. Vx2 + Vy2 = V2, tan q = Vy / Vx
  4. V = (Vx2 + Vy2)½, q = tan-1 (Vy / Vx)


What is each variable in constant acceleration equations?

  1. v = vo + a t
  1. x = xo + vo t + ½ a t2
  2. v2 - vo2 = 2 a (x - xo)
  3. v: velocity at time t, vo: initial velocity, a: acceleration at time t, t: time, x: position at time t, xo: initial position,


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?

  1. Solve one of the following equation for time t
  2. x = xo + vo t + ½ a t2
  3. t = (v - vo) / a


How to solve a question of ‘How far will the object travel …?’ under a constant acceleration?

  1. Solve one of the following equation for position x
  2. x = xo + vo t + ½ a t2
  3. v2 - vo2 = 2 a (x - xo)


How to solve a question of ‘What is the velocity of the object …?’ under a constant acceleration?

  1. Solve one of the following equation for velocity v
  2. v = vo + a t
  3. v2 - vo2 = 2 a (x - xo)


How to solve a question of ‘What is the acceleration of the object …?’ under a constant acceleration?

  1. Solve one of the following equation for acceleration a
  2. x = xo + vo t + ½ a t2
  3. v2 - vo2 = 2 a (x - xo)
  4. v = vo + a t


What is optimal angle of release?

  1. Angle of release for the maximum length of a projectile travel
  2. Depends on the vertical position of release and the vertical position of landing
  3. 45º


How to calculate torque?

  1. Forces cause translations
  2. Moments (a.k.a. “torques”) cause rotations
  3. Moments caused by a force acting at a distance from an axis of rotation: M = F · d
  4. Units of moment are force times distance, N m, or “newton-meters”


Examples of the first, second and third class levers in a human body?

  1. First: neck joint
  2. Second: ankle joint for plantar flexion
  3. Third: elbow joint for flexion

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Which class levers are the most common in a human body?

Third class levers

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What is Newton’s 1st, 2nd, and 3rd Law in their angular forms?

  1. First: q = qo + ωo t + ½ a t2
  2. Second: ω = ωo + a t
  3. Third: ω2 - ωo2 = 2 a (q - qo)


How to calculate a muscle force during a static action?

  1. Create a “free body diagram”
  2. Shows only body of interest and forces applied to it
  3. Use ∑F = 0 and/or ∑M = 0


What is the ‘force-velocity trade-off’?

  1. Most of the lever systems in a human body have inefficiency in muscle force use
  2. However, the systems have an advantage of velocity at the endpoint


What is moment of inertia?

  1. Moment of inertia (I) is to angular motion what mass is to linear motion.
  2. Moment of inertia depends on the mass and its distribution.


How to calculate moment of inertia.

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In layman's terms, what does the moment of inertia measure?

How hard is it to rotate a body.


  1. Why do track-and-fields sprinters bend their knee joints during 100-m dash?

  1. To decrease moment of inertia
  2. Moment of inertia for the human body can be changed
  3. Gymnastics and diving –
  4. Moment of inertia for twisting is smaller/larger than moment of inertia for somersaulting.
  5. Figure Skating
  6. Spinning with arms outstretched is slower/faster than spinning with arms held tight to body
  7. Running/walking/marching
  8. Easier/harder to rotate leg at hip with knee bent than with knee straight


What is momentum?

  1. Momentum
    1. amount of motion
    2. mass multiplied by velocity (P = m·v)
  2. 2nd Law gives:

i.  F = m a = m (v2 - v1) / (t2 - t1)

ii. F = (m v2 - m v1) / (t2 - t1)

  1. With no force applied, rate change of momentum is zero: Momentum is conserved. i. 0 = (m v2 - m v1) / (t2 - t1)

ii. m v2 = m v1


How to calculate momentum?

  1. P = m·v
  2. important in giving & receiving impact, collision, etc.
  3. vector
  4. unit: kg·m/s


What is impulse? How do you calculate impulse?

  1. The accumulated effect of force exertion over a period of time
  2. Change in momentum
  3. J = F·t
  4. J = DeltaP, which can be proven to equal the above equation by multiplying it by t/t



  1. How do figure skaters control their angular velocity about a vertical axis during spinning given that the angular momentum is constant?

  1. Angular momentum H = I ω
  2. With no moment applied, angular momentum is conserved: I1 ω1 = I2 ω2
  3. Angular velocity can be changed by changing moment of inertia.
  4. when I increases, ω must decrease
  5. when I decreases, ω must increase


What is the coefficient of restitution for two colliding objects?

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What is the Coefficient of Restitution for a bouncing object?

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What are the formulas for mechanical power?

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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.


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Explain the parallel axis theorem.

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What are the rules for drawing a free body diagram?

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What are centrifugal, and centripetal forces?

A fictional force.


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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.

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What are the methods for calculating COM?

  1. Suspension Method
  2. Board and Scale Method
  3. Segmentation Method


Explain Mechanical Advantage.

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Moments vs Moment arms

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