Biomechanics Final Exam

Kinematics

The description of motion without considering the cause

6 concepts of kinematics

Position, velocity, acceleration, time, trajectory, and displacement.

What information can be gained from a stick figure? Is a stick figure kinetic or kinematic?

can convey information about motion and body positioning. It is kinematic.

An object is swinging around in a circle (as in the picture below), where is the highest linear velocity observed, point A or point B?  Where is the highest angular velocity observed, point A or point B?   

Point B the same at both point

If a dropped ball has a negative acceleration, what does that mean (is it accelerating or decelerating?) How many possible explanations are there for a negative acceleration and what are they (answer in terms of direction of displacement and increasing or decreasing velocity)? How many possible explanations are there for a positive acceleration and what are they?

A dropped ball with negative acceleration is accelerating downward, meaning it speeds up as it falls. Two possible explanations; increasing velocity in a negative direction and decreasing velocity in a positive direction. Two possible explanations; increasing velocity in a positive direction and decreasing velocity in a negative direction.

You throw a ball up into the air. In phase A, it is moving upwards, and in phase B, it is moving downwards. Describe the displacement, velocity, and acceleration during phase A and phase B. 

1. Displacement: Phase A – Y increases; Phase B – Y decreases

2. Velocity:Phase A – Vy is decreasing; Phase B – Vy is increasing 

3. Acceleration: Phase A – Ay is -9.81 m/s/s; Phase B – Ay is -9.81 m/s/s

Graphical differentiation: You are looking at a time series, and you see that displacement peaks at about 2 seconds. When displacement reaches a peak, what is velocity (answer either: positive, negative, zero)?

Zero

Graphical differentiation: What has occurred in the displacement when velocity reaches a peak (answer in terms of peak, zero crossing, inflection point, positive slope, negative slope)?

Inflection point

Which is greater velocity: 118 m/s or -150 m/s? 

-150 m/s

What are the three factors affecting the projectile trajectory?

projection angle, projection speed, projection height

which of the 3 factors govern the shape of trajectory?

The projection angle governs the shape of the trajectory, influencing how high and far the projectile will travel.

which of the 3 factors govern the size of the trajectory?

The projection speed governs the size of the trajectory, determining how quickly the projectile rises and falls.

What is the optimal projection ange?

Depends on projection height; at 0 m, 45 degrees; > 0 m, <45 degrees

Why don’t athletes perform long jump att he optimim projection angle?

Athletes will most likely have to decrease horizntal velocity to achieve optimum projection angle; but speed is more important than projection angle for long jump.

Which factor is most important to optimize projection range?

projection speed

What are the equations of constant acceleration used for? In these equations, what is vertical acceleration? What is horizontal acceleration? What does constant acceleration mean?

-9.81 m/s/s, 0 m/s/s, it means is is not changing; both vertical and horizontal acceleration are constant during projectile motion

what part of the airborne system follows the projectile trajectory?

COM

can the projectile trajectory be modified once the person is in the air?

No, the trajectory cannot be modified.

Can a person change thoer reach hieght once they are in the air?

yes

Assuming projection height, angle and speed are constant, will a person jump farther if, during the flight, he hyperextends the shoulders or flexes the shoulders? 

1. Hyperextends the shoulders

2. After hyperextending the shoulders during flight phase, the person must flex shoulders before landing so that they don't fall backwards

Assuming the three factors are constant, will a person jump higher if, during the flight, she flexes both arms or has one arm flexed while the other is extended? Note we are ignoring the role of the arms in generating momentum for this question; this question focuses on just changing COMposition and how that affects jump height. 

One arm flexed while the other is extended

Indicate if the following are relative or absolute angles:

1. Relative on left (knee angle in a sit up position)

2. Absolute on right (back and feet aligned in a sit up position)

How are linear and angular velocity related and how do they apply to projectiles? For example, think of a baseball bat and batter. Projectile motion is linear kinematics; which projectile factor will optimize projectile range? The batter makes contact with the ball by swinging the bat angularly. If the ball-bat contact point is closer to the end of the barrel (point A) or closer to the handle (point B), how does it affect linear and angular velocity of the bat? How does this in turn affect linear batted ball speed? Does this also affect control of the bat? 

It's like a baseball bat, angular velocity (how fast the bat rotates) directly influences the linear velocity of the bat’s end, which in turn affects the linear velocity of the ball upon contact. 

Write this equation in words: v = rω. (v = linear velocity, r = distance from axis of rotation to point of measurement, ω = angular velocity) Use the bat example. For example, should a person use a shorter or longer bat to increase linear velocity?  Is there a possible drawback to this?

The linear velocity (v) of a point on a rotating object is equal to the distance (r) from the axis of rotation to that point multiplied by the angular velocity (ω) of the object. In the bat example, to increase the linear velocity at the end of the bat (the point where it would hit the ball), one should use a longer bat. A longer bat means a larger 'r' value, and with the same angular velocity, the linear velocity 'v' at the end of the bat will be higher. 

What is the equation for force? What are the units?

1. F = ma

2. Newtons (N)

Are weight force and acceleration due to gravity the same thing? (Hint: what are the units of force vs acceleration?)

Weight force has units of Newtons, and acceleration due to gravity has units of m/s/s. So they are not the same thing. People regularly use the term ‘gravity’ to refer to the weight force (Weight = mass times gravity), rather than saying weight force and force due to the acceleration of gravity

Understand the difference between mass and weight. What are the units? Which one changes on other planets?

Mass – kg and slugs; Weight – N and lbs; only weight changes on other planets

What is used to represent a force on free body diagrams (FBD)?

A vector

What force is always vertical?

weight

What force is always parallel to the contact surface?

friction,, it can be any direction

What are the three elements of a force vector?

1. Magnitude

2. Direction

3. Point of application

What are the units of moment arms

Units of length

moment of force

The turning effect of a force on an object around a specified axis or point.

moment

The turning effect of a force on a body, measured by the force's tendency to cause rotation

torque

The measure of the rotational force acting on an object, often synonymous with moment, that results in a twisting effect around an axis.

Units for moments of force

Newton-meter (Nm)

Why is it harder to hold the barbell in the figures on the right? Does the weight change? Answer in terms of moment of force and moment arm.  

no

What is the definition of mechanical work? What are the units?

1. Energy transfer resulting from a force acting over a distance. It's a fundamental concept in understanding how muscles and the musculoskeletal system produce movement and the energy cost of activities like walking or running. Essentially, it's the measure of how much energy is spent to move an object or body segment against a force. 

2. Units: Joule (J).

Can work be zero, if a force is applied to a body? (hint: think of pushing against a solid wall. You push all day, until you are completely exhausted. The wall did not move. What is displacement? So, what is mechanical work? Recall that mechanical work does not reflect metabolic costs.)

1. Yes, work can be zero even if a force is applied. Work is defined as force multiplied by displacement, and if the displacement is zero (like pushing against a stationary wall), the work done is also zero. Mechanical work focuses on the energy transferred by a force causing movement, and doesn't account for internal energy changes or metabolic costs. 

2. W = F x d

3. Pushing a stool

When does an applied force do zero work? (hint: look at the equation)

An applied force does zero work when it is perpendicular to the displacement and or there is no displacement. 

Is work positive or negative during a concentric contraction?  An eccentric contraction?  An isometric contraction?

1. Eccentric: positive 

2. Concentric: negative 

3. Isometric: positive and negative

Define power, what are the units?

1. The rate at which work is done, or the rate at which energy is transferred or converted. 

2. Units: Watts (W) 

What kinds of sporting activities require high power production?

Jumping, sprinting, throwing, track, cycling, wrestling, gymnastics, speed skating, canoeing, kayaking and sprint swimming

Define energy, what are the units?

1. The capacity to do work

2. Units: Joules (J)

What are the two forms of mechanical energy?  Define them.

1. Kinetic energy: the energy of motion

   1. Energy of movement

   2. ½ mv^2

2. Potential energy: stored energy based on an object’s position and configuration

   1. Position

   2. Mgh

Define moment of inertia?

The way an object resists changes in its rotational motion.

What two components influence the moment of inertia? 

Mass (m) and radius of gyration (k); you will get these answers from the provided equations.

Which is more important? mass or radius of gyration? why?

k – because it’s squared; a 10% change in k will have a greater effect on than a 10% change in mass.

Know that the radius of gyration is a 

distance (i.e. the units are in meters). The radius of gyration provides information about how the mass is distributed about the axis of rotation.

For the top 3 figures, in which situation is the moment of inertia about the axis of rotation the greatest?

The second one  because as they were spinning they increased momentum therefore the inertia has increased.

For the bottom 2 figures, in which situation is the moment of inertia about the axis of rotation the greatest?

The second one because when your arms are out the inertia is greater due to a greater force acting against the rotation. 

Define angular momentum?

1. The measure of a rotating body's resistance to changes in its rotational motion, essentially its "spinning inertia"

2. When you twist one way and then go the opposite direction

3. It is conserved

4. Conservation is a key concept

What three factors affect the body’s angular momentum? 

Mass (m), k, and angular velocity (w); you will get these answers from the provided equations

Angular velocity must be in what units in order to calculate angular momentum?

rad/s

A diver leaves the diving board with angular momentum of 30 kg.m²/s and moment of inertia of 10 kg.m².  

You must know that the angular momentum with be 30 kg. m²/s throughout the entire dive. The moment of inertia will change as the person changes the position of their limbs. You must know when they will spin faster and when they will spin slower (angular velocity).

Can a diver, after completing rotations, enter the water with zero angular velocity? 

No

What does the diver alter in order to change the angular velocity? 

Position of their body segments

If a person is in free-fall with zero angular momentum, and she rotates her arms in a counter-clockwise direction, what direction does the body move, counter-clockwise or clockwise?

The body would move clockwise due to the principle conservation of angular momentum.

In order to keep the angular moment constant (Conservation of angular momentum), a rotation of body segments will result in a compensatory rotation of other segments.  In which direction is the compensatory rotation, the same direction, or the opposite direction? (Hint think of the rotation platform)

Opposite direction

Can a cat violate the Conservation of Angular Momentum? 

NO

Define posture and the units

1. The study of the mechanical principles governing the movement and form of living organisms. 

2. Units: angles and distance

Know two definitions of stability 

resistance to disruption of equilibrium; resistance to linear and angular accelerations

Know the definition of balance 

ability to control equilibrium

List 4 factors a person can change to increase stability.  Give an example of each.

1. Base of support: Widening stance while standing.

2. Center of gravity: Lowering body while bending knees.

3. Weight: Reducing body mass through exercise.

4. Sensory input: Improving vision through proper lighting.

Is standing still mechanically stable or unstable?

mechanically unstable

Define the center of pressure (COP).  What are the units?

1. The point where the ground reaction force is considered to be acting. 

2. Cm and mm

Define center of mass (COM).  What are the units of COM?

1. The point where the mass of an object or system is concentrated. It's the weighted average position of all the mass in a system. 

2. Units are m

Moving the COP will alter another quantity – what is that quantity?

the center of mass (COM)

In a passive system (one without muscles or a motor; e.g. a box), if the COM is pushed outside the base of support, what happens? 

The system will topple or fall over due to loss of balance, as the center of mass no longer aligns with the base of support.

When a person initiates gait (starts walking), the COM moves outside the BOS.  Why don’t they fall down?

The individual maintains balance by shifting their body weight and adjusting the position of the center of mass relative to the base of support (BOS). In this way, the person compensates for the shift to prevent falling.

List three reasons humans are mechanically unstable.

1. High center of mass relative to base of support.

2. Narrow base of support when standing or moving.

3. Dynamic movements that disrupt balance.

Sensory systems provide redundant information.  What does this statement mean?

It means that multiple sensory modalities (like vision, proprioception, and vestibular input) can provide similar information about body position and movement, enhancing balance and stability.

For persons using a cane while walking, make sure you understand the relationship between the cane, center of mass and base of support. Why is the cane carried beside the sound limb?

The cane is carried beside the sound limb to support weight and enhance balance, effectively widening the base of support and helping to control the center of mass during gait.

Imagine you are walking with a client who has compromised balance. You are concerned because they are unsteady. What can you do to increase their base of support

You can encourage them to adopt a wider stance, use assistive devices for support, and practice weight shifting exercises to improve stability.

Define biomechanics. 

Science that applies mechanics to biological systems

statics

Study of bodies at rest The system is either: • not moving OR • moving at a constant velocity 

dynamics

study of bodies in motion and the forces that affect them.

kinematics

description of motion without regard to the cause of motion

kinetics

study of the causes of motion (primarily the study of forces)

system

a biological system that is studied using the principles of mechanics

kinematic quantities

displacement, velocity, acceleration, and time

kinetic quantity

forces and moments of force

Are these qualitative or quantitative: He jumped very high, the man walked very slowly, leaning to the left, his gait was asymmetrical.

Qualitative

Are these qualitative or quantitative: He jumped 50cm

Quantitative

superior

closer to the head

• the shoulder is______ to the hip

inferior

Farther away from the head; the knee is _____ to the hip

Anterior

Toward the front of the body; he nose is ______ to the ear

Posterior

Toward the back of the body; the spine is _____ to the sternum.

medial

Toward the midline of the body; the nose is _____ to the cheeks.

lateral

Away from the midline of the body; the ears are _____ to the eyes.

proximal

Toward the point of attachment or origin; the elbow is ______ to the wrist. (closer to the trunk)

distal

Away from the point of attachment or origin; the wrist is ____ to the elbow. (away from the trunk)

superficial

toward the surface of the body

deep

inside the body

prone

lie face down

supine

lie face up

abduction

lifting the arm

adduction

the arm is at your side

flexion

when the limb is lifted up

extension

the limb is moved back; example: your arm resting at your side