FINAL KIN 3514 KIM
Vertical GRF
"M" shaped curve • The vertical GRF can be split into four
A figure skater generates a torque of 76 Nm over 0.23 s during the take-off of a jump • If the skater's moment of inertia is 4.27 kg·m2, what is the skater's angular velocity at take-off?
(Assume an angular velocity of 0 before the moment is applied) 𝑓𝑖(76)(0.23) = (4.27)𝜔 − (4.27)(0) 17.48 = 4.27ω ω = 4.09 rad/s
Law of Cosines
(useful if you have the segment lengths, or points for 3 joints) Step 1: Calculate the length of each side - Step 2: Calculate cosine theta𝛉 a= sqrt(x3-x2)^2 + (y3-y2)^2 b=sqrt(x2-x1)^2 + (y2-y1)^2 c^2 = a^2+b^2 - 2ab (cos theta)
Relative angle of the hip joint
- positive angle for flexion- negative angle for extension
• Relative angle of the ankle joint
- positive for dorsiflexion - negative for plantarflexion
• Relative angle of the knee joint
- positive for flexion- negative for extension
Kinetic energy (KE)
-Defined as the energy an object possesses due to its motion Energy due to motion• The energy stored in a moving object
θ in radians
-The angle at the center of a circle described by an arc equal to the length of the radius θ = arc length/radius s/r
Potential energy (PE)
-stored energy due to position or deformation Gravitational Potential Energy: the energy stored due to an object's position above the ground Strain Energy: the energy stored due to the deformation of the object
If the object travels ....., those rotations must be included in the displacement
1 or more full rotations
What is the angular displacement? What is the max angular displacement that can be achieved?
35 ̊ - 0 ̊ = 35 ̊ →70 ̊-0 ̊= 70 ̊
he acceleration threshold for a concussion is estimated to be
81 g (= 785N).
the knee joint travels through 85.95° of angular displacement in 2 sec, and the lower leg is 0.5m long. What is the tangential velocity?
85.95° = 42.98° 2𝑠𝑒𝑐 1𝑠𝑒𝑐 𝑣𝑡 = 𝑟𝜔 = 0.5m X 0.75rad/sec = 0.375 m/sec Angular velocity of all points on the segment is 0.75 rad/sec angential velocity of the point of interest is 0.375 m/sec = 85.95° = 42.98° ∆𝑡 2𝑠𝑒𝑐 1𝑠𝑒𝑐 𝑣𝑡 = 𝑟𝜔 = 0.5m X 0.75rad/sec = 0.375 m/sec
-Given the 2D coordinate (x,y) of the knee and ankle, calculate the absolute angle of the lower leg. θ = 𝐭𝐚𝐧−𝟏(y knee - y ankle / x knee - x ankle)
= 𝐭𝐚𝐧−𝟏 (0.51 - 0.09 / 1.22 - 1.09) = 𝐭𝐚𝐧−𝟏 (0.42/0.13) = 𝐭𝐚𝐧−𝟏(3.23)= 1.27rad θ leg = 1.27rad x 57.3 = 72.8°
Calculate the angular displacement of a circular track that has a radius of 9m and covers a total distance of 185m?
=185m/9m =20.56 rad theta=s/r s: distance covered along the circle path • r: Radius of the circular path
Concentrated forces
A force acting at a single point
Choose the answer that has the highest impulse A. A force of 90 N applied over 2 seconds b. A force of 10 N applied over 20 seconds c. A force of 200 N applied over 1 second d. A force of 70 N applied over 3 seconds
A force of 70 N applied over 3 seconds
Distributed forces:
A force that is applied over a distributed area • If an object experiencing a force is deformable, the force may be distributed throughout the object.
Examples: Second-class Levers
A large resistance can be moved by a relatively small force • Door • Wheelbarrow • Nutcracker • Loosening a lug nut
What is a force
A push or a pull
Parkinsonian Gait
Also known as Festination gait or Propulsive gait
Ataxic Gait
Also known as cerebellar gait, unsteady gait
Sensory Gait
Also known as stomping or stamping gait
Hitting the ball with the club head vs. with the shaft Which one produces the faster velocity?
Because the club head is farther from the axis of rotation, the 𝒗𝒕 of the club head (𝑣𝑏) is faster than the 𝒗𝒕 of a point on the shaft (𝑣 ) 𝑎
Initial contact / Heel strike
Beginning of the stance phase when part of foot is in contact with ground (usually heel contact) Weight acceptance phase Gait cycle • 0%-2% Function • Position the limb for stance • Motion (Relative angle) • Hip = Flexed 20-30 ̊& Externally rotated • Knee = Extended/ 5 ̊ flexion • Ankle = Dorsiflexed/Neutral • Foot = Neutral
Initial swing / Acceleration
Begins when toe off is complete and the reference limb swings until positioned directly under the body
Efficiency of Gait
Body COM is going up and down as you lift up your leg /or swing your leg
Posterior peak
Braking peak in the loading response The posterior peak should normally be on the order of 0.2 times the person's body weight
Net Force
Combination of all forces acting on an object
Hemiplegic Gait
Commonly seen in patients who have experienced a stroke
Conversion
Convert radians to degrees, or degrees to radians 72°/57.3° =1.26rad 1.26 rads x 57.3° = 72°
kinetics
Deals with the Causes of Motion • When forces act on a body, this causes either linear motion or angular motion
Step length
Distance from Initial contact on the foot to initial contact on the opposite foot. 1/2 of stride length
Stride length
Distance from initial contact to initial contact of the same foot.
Radius of Gyration (k)
Distance from to axis of rotation to a point where the segment's CoM Radius of gyration can be changed depending on the body posture
Running Gait Cycle
Double support disappears, 'Double swing' develops • Flight (swing) phase in running • Ratio stance/swing reverses
Anterior-Posterior GRF
During the gait cycle of walking, the body undergoes repeated cycles of braking and propulsion as the foot makes contact with the ground and then lifts off again.
Conservation of Mechanical Energy
Energy cannot be destroyed, but only transferred from one form to another form In the absence of externally applied forces other than gravity, the total mechanical energy (sum of KE and PE) of a system remains constant
A gymnast jumps up and grasps the bar, and his coach stops his swinging by exerting forces on the front and back of the gymnast's torso. • External forces• Coach stops his body swinging = 30N+20N • Upward vertical reaction force = 550N • Force of gravityGymnast's mass = 51 kg = 500N Q: What is the net external force acting on the gymnast?
Equation x: 30N + (-20N) = 10N y: -500N + 550N = 50N ө 10N Counterclockwise + Clockwise Pythagorean theorem A2 + B2 = C2 (10N)2 + (50N)2 = C2 100N2 + 2500N2 = C2 2600N2 = C2C = 51 N Resultant force = 51N
Example - Helmets DJ falls off his horse and strikes his head on the ground. Fortunately, he is wearing a helmet. • Impact force on DJ's head is 5606N. The mass of his head is 5 kg. • Did the helmet protect DJ from concussion?
F = ma 5606 N = (5 kg)a a = 5606 N/ 5 kg a = 1121 m/s2 Dividing this value by (9.81 m/s2)/g will give us acceleration in terms of g: a= 1121m/s2 9.81 m/ s2 a=114g
Static Equilibrium
If an object is at rest, it is in a state of static equilibrium • For an object to be in static equilibrium, the external forces (or torque) acting on it must sum to zero ∑𝐹 = 0 ∑𝜏 = 0
.... done by the external forces on a system is equal to the change of kinetic energy
Net work 𝑤 =Δ𝐾𝐸 𝑛𝑒𝑡
Law of Acceleration
Newton's 2nd law: an object will move in the direction of the force applied to it F=ma
Walking base (Width)
The side-to-side distance between the line of two feet, usually measured at the midpoint of the heel.
torque
The tendency of an eccentric force to make an object rotates around an axis
Stride time
The time elapsed between foot contact of a leg to the following foot contact of the same leg.
Double limb support
Two intervals during gait cycle and both feet are in contact with ground
UNITS
Uses Degrees or Radians to describe angular motions • Degree: 360° in a circle • Radian (rad): the ratio between the length of an arc & its radius in a given circle, θ = 1 rad • 1 radian = 57.3 degrees
Stress
Vector • Defined as the internal resistive force to the deformation per unit area
Mechanical work while walking stairs • When this person reaches the top of the stairs, 2355 J of work is done, and this person is displaced 3 m up →Positive work
W = (785N)(10×0.3m) W = +2355J
Segment Method
Weighted average of all segments summed together in space
In an elastic collision, ............of the system are conserved. On the other hand, in an inelastic collision,......
both the momentum and the kinetic energy momentum is conserved but kinetic energy is not.
Angular impulse
change in angular momentum
impulse=
change in momentum
The .... is a measure of the amount of friction existing between two surfaces
coefficient of friction, μ,
In many sports, .... between players or between players and playing surfaces or other objects ....
collisions produce large accelerations that may result in head injuries.
Forces in collisions
Whenever a moving object comes into contact with another object, we can call this event a collision Principle of Conservation of Linear Momentum
What is the weight of the Trunk of a female weighting 67kg?
m = (0.448) × 67kg m = 30 kg
EX. What average net force must a baseball player catcher apply to a 35.8m/s pitch to stop it over a time of 0.025s? mass =0.13
m = 0.13 kg t = 0.025 s vi = 35.8 m/s vf = 0 m/s F = ?? Step 2: Equation • F = ma• a = (vf- vi)/t Step 3: Substitute the known quantities • F = ma = 0.13 kg × (0 m/s - 35.8 m/s )/0.025 s = -186.16 N Can we have a negative force?
If we consider this event to be a perfectly inelastic collisions, what is the velocity and direction of the players after the impact? person 1 m=90kg v=6 m/s person 2 m=80kg v=7m/s
m1v1 + m2v2 = (m1 + m2) 𝑣 (90 x 6) + (80 x -7) = (90 + 80) x v 540 - 560 = 170 x v v=-20/170v= -0.12 m/s
elastic collision formula
m1v1 + m2v2 = m1v1' + m2v2'
When the golf club hit the ball at 270m/s, then the ball flies at 360 m/s • How much does a golf club slow down after a collision?
m=0.2 kgVi = 270m/s Vf = ?? Vf= 360 m/s
Density =
mass/volume
inelastic collision formula
m₁v₁ᵢ+m₂v₂ᵢ=(m₁+m₂)vᶠ
Friction is a
necessity and a hindrance
clockwise =
negative
The effects of these forces are______by each other because they act on different objects
not canceled
Does size dictate inertia
not completely
Question: How much kinetic energy does a baseball have when thrown at 36.7 m/s?- A baseball's mass is 0.145 kg
olution: 𝐾𝐸= 1𝑚𝑣2 2 𝐾𝐸 = 1 (0.145𝑘𝑔)(36.7 𝑚/𝑠)2 2 𝐾𝐸 = 97.6 𝐽
Forces always come in..
pairs
Friction
parallel to thee surface -slide across each other
During this .... motion, energy is constantly being generated, so theoretically it should never stop.
pendulum
Normal force -contact
perpendicular to the surfaces -pressing against each other
When performing a bicep curl, on the way up the biceps produce _____ work and on the way down the biceps produce work
pos, neg
Counter clockwise =
positive
The outcome of these collisions can be explained with the
principle of the conservation of momentum
The average velocity is the
product of cadence and stride length.
Momentum
quanity of motion m=mass x velocity
Mass
quantity of matter units : kg
Which one affects angular momentum the most?
radius of gyration (k); because it's squared
tangential acceleration
rate of change of linear velocity caused by angular acceleration vt=rw instantaneous linear velocity of an object in rotational motion. Only valid if 𝜔 is expressed in rad/sec a𝒕 = 𝑟α the linear acceleration resulting from angular acceleration. Only valid if α is expressed in rad/sec2
Balance
refers to an object ability to maintain a steady position without falling over
Ineretia
resistance to a change in motion directly proportional to mass
Only internal forces can change the ______ of the system
shape
ach gait cycle, for each leg, is divided into two phases,
stance & swing.
Force can cause an object to
start, stop, speed up, slow down, or change direction
The -.... increases as the applied force increases, always equal to the net applied force.
static friction force
Spatial (distance):
step length, stride length, width, toe-out angle etc.
Temporal (time):
step time, stride time, speed, cadence (steps/min) etc.
Velocity formula
stride length (m) x 1/2 x steps/min x min/60s
μ > 1, the frictional force is
stronger than the normal force →hard to slip
Example of law of interim
table cloth trick
Relative angle can be determined from
the absolute angles 𝛉Hip=θtrunk+(180 −θthigh) 𝛉 𝐊𝐧𝐞𝐞 = θ shank + (180 − θ thigh) 𝛉 Ankle = θ shank + (180 - θ foot)
Newton's 2nd law of motion
the acceleration of an object depends on its mass and force -impulse-momentum relationship -increasing the duration of force application increases the duration of force application increases the change in momentum
Volume
the amount of space that something occupies SI units are m3 (cubic meter) (or liter)
CoM of the human body
the height of the CoM is 55% to 57% of your standing height in anatomical position The position of the CoM change depending on posture
acceleration
the observed change in motion
Swing phase:
the period of time when the foot is moving forward through the air make up 40% of cycle Foot of reference extremity is in contact with ground
Stance phase:
the period of time when the foot is on the ground (more reliable information) make up 60% of cycle Foot of reference extremity is in contact with ground
If the LoG falls outside of the base of support...
the person must provide corrective muscle action, otherwise they will fall
Consider three balls, ping pong ball, tennis ball, bowling ball. if each is hit with the same amount of force, which accelerates the most and why?
the ping pong ball, because it is lighter in mass
In a perfectly inelastic collision,
the total momentum is conserved, but total (kinetic) energy is not conserved.
When the total angular momentum is conserved,
there is a tradeoff between these two
Ex. of impulse
throwing an egg onto sheet dropping egg from 10m height
Two absolute angels
to find relative angles (useful if you have two absolute angles) θrelative= 𝛉 absolute leg + (180 - 𝛉absolute thigh) θrelative= 72.8° + (180 - 105.41°) = 147.4°
Inelastic collision
two separate objects collide and then combine and move together as a single mass.
An individual is skating around a turn with an 11 m radius at 3.75 m/s. What is the skater's centripetal acceleration?
v = 3.75 m/s r = 11 mac = v2/r ac = 3.752/11 = 14.06/11 =1.28m/s2 Centripetal acceleration will increase if radius decreases or if velocity increases• Tighter the turn, the more you're pulled to the center
The ____ of the projectile is constantly changing , due to the force of gravity ...law of inertia does NOT apply
vertical velocity (up or down)
Noncontact forces
when forces are not touching each other
Contact forces
when forces are touching each other
Principle of conservation of momentum:
when two objects collide and no other external forces act on them, total momentum of the system remains constant.
A .... is approximately 55% of her height from the ground, whereas a man's CoM is approximately 57% of his height from the ground
woman's CoM
Angular Motion
ystems rarely move in purely linear motion • involves some degree of rotation • refers to motion around an axis of rotation
As radius of rotation r increases.. ...
• Arc length s increases for a given angular displacement θ Tangential velocity 𝑣𝑡 increases for a given angular velocity 𝜔
Temporal parameters
• Stride time• • Cadence (step rate)• • Gait speed•
Effort (muscle force)
• moves the lever
Fulcrum (joint)
• the axis around which the lever pivots
Lever Resistance Resistance (weight or load)
• the force or weight that is being lifted or moved by the lever
if 𝜔 = 600 ̊/s, and the arm is 60cm long, what is the tangential (release) velocity?
• 𝜔 = 600 ̊/s→600/57.3 = 10.47 rad/s • 𝑣𝑡 = 𝑟𝜔 = 0.6m × 10.47rad/s 6.28 = 6.28 m/s
If a segment of the body travels 45° and the interval is 1.5 sec, what is the angular velocity?
→𝜔=45°/ 1.5s= 30°/sec (or 30/57.3 = 0.52 rad/sec) →The greater the rotation angle in a given amount of time, the greater the angular velocity
Computing Angular Displacement
∆𝜃= (𝜃f −𝜃i) +𝑛 × 360°
Balanced forces
∑F = 0 • No change in motion • No change in direction • Object either at rest or moving at a constant velocity Balanced forces = no acceleration
unbalanced forces
∑F > 0 • Change in motion • Change in direction
Find the CoM of the entire arm
∑𝑚 seg∙ 𝐶𝑜𝑀seg/total mass (9𝑘𝑔 ∙3) +(8.6𝑘𝑔∙5)+(2.4𝑘𝑔 ∙7)=4.34 20 𝑘𝑔 9𝑘𝑔 ∙7 +(8.6𝑘𝑔∙4)+(2.4𝑘𝑔 ∙5)=5.47
How much force the biceps generate to support the weight of the forearm and the book?
∑𝜏 = 0 𝑟1𝐹b +(−𝑟2𝑤a)+(−𝑟3𝑤b)=0 r1fb= r2wa + r3wb Fb= rwwa+r3wb/r1 Fb= (0.16m)(2.5kg)(9.81m/𝑠2)+(0.38m)(4kg)(9.81m/ 𝑠2) =470N
A 60kg diver• 6 rad/s about transverse axis in a layout position• Moment of inertia is 15 kg·m2 during layout• 24 rad/s during tuck Q: What is her radius of gyration in the tuck position?
𝐇layout = 𝐇𝐭𝐮𝐜𝐤 (15 kg·m2)(6 rad/s) = (60kg)(𝐤𝟐 tuck)(24 rad/s) 𝐤𝟐 tuck = (15 kg·m2)(6 rad/s) /(60kg)(24 rad/s) 𝐤𝟐 tuck = 0.0625 m2𝐤 tuck = 0.25 m
A 4kg brick is sitting on a table. The coefficient of static friction between the surfaces is 0.45. • What is the largest force that can be applied horizontally to the brick before it begins to slide?
𝐹 = 4kg × 9.81m/s^2 𝑛 = 39.2 N μ𝑠 = 0.45 F = 0.45 × 39.2 𝑓𝑟 F𝑎𝑝𝑝 = 17.64 N
How much strain energy is stored in a tendon that is stretched 5 mm (0.005 m) if the stiffness of the tendon is 10,000 N/m?
𝑆𝐸 = 1 𝑘Δ𝑥2 2 𝑆𝐸 = 1 (10,000 N/m)(0.005 𝑚)2 2 𝑆𝐸=0.125J
If a segment with a circle radius of 1 meter, 2 meters, and 3 meters, respectively, rotates 90 degrees, what would be the length of the arc?
𝑠 = 1.57 rad × 1m 𝐴 = 1.57m 𝑠𝐵 = 1.57 rad × 2m =3.14m 𝑠𝐶 = 1.57 rad × 3m =4.71m
Third-class Levers in human body
Most common in human body • ≈85% of the muscles in the body function as third class levers
Calculate the absolute angle of the thigh In which quadrant is the thigh part?
hip (1.14, 0.8) Knee (1.22, 0.51) θ𝐭𝐡𝐢𝐠𝐡 = 𝐭𝐚𝐧−𝟏(y hip- y knee/ x hip - x knee ) = 𝐭𝐚𝐧−𝟏(0.8 - 0.51)/(1.14 - 1.22) = 𝐭𝐚𝐧−𝟏 -3.625 = - 74.58° = - 74.58° + 180° = 105.41° (relative to the right horizontal)
The _____ velocity of the projectile is constant and its acceleration is - , constant, because no horizontal forces acting on the projectile
horizontal (left or right)
Law of Inertia
if no net external force acts on an object, that object will not if it was not moving or it will continue moving at constant speed in a straight line if it was already moving
The application of an ____ results in a change in the ____ of a body
impulse momentum
Radial acceleration
inward acceleration necessary for angular motion
Weight
is a measure of how the force of gravity acts upon that mass Vector 𝐹 =𝑚𝑔
Line of gravity (LoG)
is an imaginary vertical line from the CoM to the ground or surface the object or person is on
Linear velocity direction
is at a tangent to the curved path and perpendicular to the rotating object
Base of support (BoS)
is the area around the outside edge of the sections of your body in contact with the ground/surface
Stability
is the capacity of an object to return to equilibrium or to its original position after it has been displaced
Potential energy (PE) 𝑃𝐸 = 𝑚𝑔h PE = gravitational potential energy (J)M = mass (kg)g = acceleration due to gravity = 9.81 (𝑚/𝑠2) h = height (m)
is the energy (capacity to do work) that an object has from its position or deformation
Ground reaction force (GRF)
is the force a person's feet exert on the ground.
Tangential velocity
is the instantaneous linear velocity of an object in rotational motion 𝑣𝑡 is termed 𝑣𝑡 = 𝑟𝜔
Work
is the product of force and the amount of displacement in the direction of that force is performed if the object is linearly displaced by the force application
angular acceleration
is the rate of change of angular velocity =delta w/delta t
Power
is the rate of doing work, or how much work is done in a specific amount of time - refers to how fast work is done upon an object. P=W/Δ𝑡
Moment of inertia
is the sum of the products of each particle's mass (m) and the radius of rotation (r) for that particle squared quantifies how difficult it is to rotate an object about an axis (i.e., resistance to angular motion) Similarly, it takes more torque to cause angular rotation of an object with a higher Mi... Mi takes into account not only the mass of the object but also how it is distributed
total CoM formula
kg x m/kg
Knee Motion: Sagittal plane
1. After initial contact 2. After first peak of knee flexion 3. Pre-swing Initial swing 5. Late swing
Hip Motion: Sagittal plane
1. Initial contact to terminal stance 2. Pre swing to mid swing 3. Terminal swing
Three factors which affect angular momentum
1. mass 2. radius of gyration (k) 3. angularvelocity(ω)
SI unit for force
1N = 1kg . m/s^2
Moments of Inertia of the Human Body
An object may have more than one moment of inertia because an object may rotate about more than one axis of rotation • Human movement may change the distribution of mass about an axis of rotation, thus changing the moment of inertia about that axis
A figure skater spins 10.2 revolutions in a clockwise direction, pauses, then spins 3.5 revolutions counterclockwise before skating away. Q. What angular distance did the skater rotate through? Q. What was the skater's angular displacement?
Angular distance = sum of all angular changes = 10.2 + 3.5 revolutions = 10.2 + 3.5 = 13.7 revolutions (or 4,932°) Angular displacement = change from start to finish = -10.2 revolutions + 3.5 revolutions = -6.7 revolutions (or -2,412°)
Eccentric force
Apply a force NOT directed through the center of an object • Cause linear and angular motions of an object
Centric force
Apply a force that directed through the center of an object • Cause linear motions of the object
Classification of Levers
Arrangement of the applied force, the fulcrum, and the resistance determines the classification
Myopathic Gait
Associated with muscle disorder
Ankle Motions: Frontal plane
At heel strike, the foot lands in a slightly inverted position and moves into eversion during loading Rapid inversion then takes place just prior to 50% of the gait cycle
ML GRF split into 3 sections
At initial contact, the foot is from a supinated position into pronation. This action generates a lateral GRF at the early stance phase After the loading response, the forces push in a medial direction as the body moves over the stance limb Small lateral forces are also often seen during the final push-off stage
Loading response / Foot flat
Foot going flat on the ground • Weight acceptance / Double limb support Gait cycle • 2%-12% Function Transfer body weight onto the limb Absorb shocks and move forward • Motion Hip = Flexion 20 ̊ & slightly Externally rotated Knee = Flexion 5-10 ̊ (primary source of shock absorption) Ankle = Plantarflexion 5 ̊/neutral (shock absorption) Foot = Eversion 5 ̊
Abnormal Supination
Foot is rolled to the outside too much and more weight is put on the lateral border of the foot. Add >12 ̊ of calcaneal inversion
Law of action and reaction
For every action there is an equal and opposite reaction -forces always occur in action-reaction pairs
Law of linear acceleration F= m ∙ a
Force = m x (∆v / t)Force x t = mass x (∆velocity / t) x t Force x t = mass x velocity Linear Impulse = Linear Momentum
The coefficient of static friction between a sled and the snow is 0.18, with a coefficient of kinetic friction of 0.15. A 250 N girl sits on the 200 N sled. • How much horizontal force is required to start the sled in motion? • How much force is required to keep the sled in motion?
Fs = μsFn Fk = μkFn Fs = μsFn= 0.18 ×(250 + 200) = 81 N Fk = μkFn= 0.15 ×(250 + 200) = 67.5 N To start the sled in motion > 81 N of horizontal force is required. To keep the sled in motion at least 67.5 N of horizontal force is required.
Does your body weight change during an elevator ride? • How does it feel when the elevator starts up or down? Do you feel heavier or lighter? →Explain this using Newton's second law of motion r=the reaction force exerted on your feet by the elevator w=weight
If R > W,• Feel heavier and the net force acts upward, resulting in an upward acceleration.• This is exactly what happens when the elevator speeds up in the upward direction: it accelerates you upward, and you feel heavier. If R = W,• Feel neither heavier nor lighter, and the net force is zero, resulting in no acceleration. If R < W, Feel lighter and the net force acts downward, resulting in a downward acceleration. This is exactly what happens when the elevator slows down; you decelerate upward, and you feel lighter
Terminal stance / Heel off
Heel is beginning to lift off • Gait cycle • 31% - 50% • Function Advance body over the stationary foot Transfer the body weight to the forefoot • Motion Hip = Extension 20 ̊ & internally rotated Knee = Extended / 5 ̊ flexion Ankle = Dorsiflexion 10 ̊ Foot = Eversion
Angular velocity
How fast the angle is changing The vector rate of change of angular displacemen w= delta theta/deltat
Density
How much matter (mass) is present per unit of volume =mass/volume, SI units are kg/m3
What is the moment of inertia of the mass on the stick? Length from point of rotation to weight, r = 0.25 m m=0.1 kg (weight in middle)
I = m × r2 = 0.1 × 0.252 = 0.0063 kg · m2
What is the moment of inertia of the mass on the stick? Length from point of rotation to weight, r = 0.5 m m=0.1kg (on top)
I = m × r2 = 0.1 × 0.52 = 0.025 kg·m2
ac=ω2r
If ω is kept constant, ac is proportional to r
ac = 𝑣𝑡2/r
If 𝑣𝑡 is kept constant, 𝑎c is inversely proportional to r
Elastic collision
In a perfectly elastic collision, two objects collide, and bounce off each other. Total momentum & (kinetic) energy of the system are conserved
Conservation of Angular Momentum
In the absence of external torques, the total angular momentum of a given system remains constant.
Justin Jefferson is traveling 8 m/s and has a mass of 89 kg. Kirk Cousins passes the ball to him at 17 m/s. If he catches the ball, what kind of collision is this?
Inelastic
Ankle Motion: Sagittal plane
Initial Contact to Loading Response Loading Response to Terminal Stance Pre-swing Initial swing to terminal swing
Static friction•
Keeps an object at rest from moving Motion
Mechanical energy comes in two forms
Kinetic energy (motion) and Potential energy (stored)
Pre-swing / Toe off
Last event of the stance phase -Second period of double limb support -Toes are just beginning to off the ground but still in contactwith the ground and the other leg is in 'loading response'. Gait cycle • 50% - 62% Function • Body prepare for swing, so more load is transferred to the other limb Motion Hip = Extension 10 ̊ Knee = Flexion 40 ̊ Ankle = Plantarflexion 15 ̊ Foot = Neutral
Medial-Lateral GRF
M-L forces are the most variable • easily affected by footwear, foot orthoses, speeds, age, weight, etc. split into 3 sections
Spatiotemporal parameters
Measures obtained from gait analysis• - Can be used for clinical evaluation / can be used to monitor change during treatment and rehabilitation programs
Advantages in First-Class Levers
Mechanical advantage in force production • Effective to increase speed or ROM • Can be more stable. A state of equilibrium can be achieved either with or without MA
Single limb support
Only one foot in contact with ground
Anything above the ground has gravitational potential energy Q: How much PE does a 700 N ski jumper have when taking off from the 90 m jump?
PE = mgh = Wh = (700 N)(90 m) = 63,000 Nm = 63,000 J
Pelvic Tilt (Obliquity)
Peaks occur during early stance and early swing • 5° dip of the swing side
lantar pressure when walking
Plantar pressure measures the compressive force exerted on the plantar surface
Player #1 is 97.5kg and traveling at 6.6 m/s. Player #2 is 104 kg and traveling at 5.9 m/s. Who is traveling with more momentum?
Player #1
Center of mass:
Point in the body where all particles are evenly distributed Therefore, the sum of the moments created by all particles in the body is equal to zero at this point
Gravitational potential energy
Potential energy from an object's position relative to the Earth • It is typically referred to as potential energy
Anterior force
Propulsion peak in the pre-swing • Produced when the foot is pushed down and back into the ground. • This force propels the body forwards
E.g., Runners at toe-off • The vertical ground reaction force (normal contact force) acting under a runner's foot is 2000 N, while the frictional force is 600 N acting forward. What is the resultant of these two forces?
Pythagorean theorem A2 + B2 = C2 (2000N)2 + (600N)2 =C2 4000000N2 + 360000N2 = C2 4360000N2 =C22088N = C Resultant force = 2088N
vGRF in stroke patients
Reduction in the 1st peak relates to • Poor confidence A high trough or shallow trough can relate to • A poor movement of the body over the stance limb Reduction in the 2nd peak relates to • A poor ability to push off
Mid swing
Reference foot is passing the contralateral leg
Why is the CoM important?
Related to stability and balance•
The ...... is used to show the direction of angular motion
Right-Hand Thumb Rule
Pressure
Scalar • Defined as the force per unit area that is exerted on a surface
Diplegic Gait (Spastic gait)
Seen in cerebral palsy (CP) Bilateral involvement
Neuropathic Gait
Seen in patients with peripheral neuropathy Also known as Steppage gait or Equine gait
Mid stance
Single limb support phase• Body weight directly over the supporting limb (single limb) • Gait cycle • 12% - 31% • Function • Advance body over the stationary foot • Motion Hip = Extension to Neutral Knee = Extended/5 ̊ flexion Ankle = slightly Dorsiflexion 5 ̊ Foot = decreasing Eversion
Gait Cycle
Single sequence of functions by one limb •Referred to as one stride (1≈second in normal GC) •Begins when reference foot contacts the ground •Ends with subsequent floor contact of the same foot
Dynamic friction
Sliding friction and kinetic friction • Created between any two surfaces when they are in a moving position
Why starting lines for the 400m and 200m staggered?
Staggered starts are needed for 200m and 400m events to ensure all competitors cover the same distance (arc length)
Which person has the most inertia (sumo wrestler vs smaller person)
Sumo , because he has a bigger mass and a greater tendency to remain in his current state of motion
Strain potential energy (SE) SE= 1/2 kdeltax^2 SE = strain energy (J) k = stiffness or spring constant of material (N/m) ∆x= change in length or deformation of the object from its undeformedposition (m)
The result of the deformation of an object • An object gains SE when it is stretched or squeezed • Also referred to as elastic potential energy or strain energy
T/F Potential energy is the energy (capacity to do work) that an object has from its position or deformation
T
T/F a system has more inertia, you will need more force to start moving it
T
Absolute Angles (segment angles)
The angle between a segment and the right horizontal of the distal end -simply draw a horizontal line at the distal end of the segment and measure the angle from this horizontal line in a counterclockwise direction
Relative Angles (joint angles)
The angle between the longitudinal axis of two adjacent segments Straight fully extended position is generally defined as 0 degrees (or can be 180) -
Toe out angle
The angle in degrees between the direction of progression and a reference line on the sole of the foot.
Angular Inertia
The angular version of the first law can be stated as follows: "A rotating body continues to turn about the axis of rotation with constant momentum unless acted upon by an eccentric force or external torque" A rotating body will remain in angular motion until another force acts upon it If ∑𝛕= 0, then ∆ω = 0
Gait Speed
The distance covered by the whole body in a given time (m/s). • Speed = distance/time
Third-Class Levers
The effort (force) lies between the resistance and the fulcrum
If the same force is applied, which cart has the greater acceleration? (empty cart vs full cart)
The empty the full cart has a larger mass than the empty cart does
trough level
The lowest point after peak
torque depends on two factors:
The magnitude of externally applied force (F) The distance that the force is applied from the axis of rotation (moment arm, d) 𝛕=Fd
Motion capture cameras
The most common method for collecting kinematic data (kinetic data measured by force plates) Components include several infrared cameras, a marker set, and software
Eccentric contraction
The muscle lengthens as it contracts Muscle force acts against the direction of the motion of muscles' insertions Negative work is performed
Isometric contraction
The muscle remains the same length No displacement of muscles' insertions in relation to each other No work is performed
Concentric contraction
The muscle shortens as it contracts Muscle force acts along the line of muscles' insertions Positive work is performed
Cadence (step rate)
The number of steps taken in a given time (steps/min, SPM). • Normal: 100 - 115 steps/min
Second-Class Levers
The resistance lies between the fulcrum and the point of effort • This lever uses mechanical advantage in force production to make moving large resistance easier
centripetal (radial) acceleration ac or ar
This acceleration (ac) is towards the center of rotation & perpendicular to the circular motion This refers to changes in the direction of the velocity but not its magnitude at affects magnitude ac affects direction ar = ω2r
Passive dynamic walker
This walker is walking down a slop, and main source of power is PE. • The source of KE is created by this person pushing.
How can these injury-causing accelerations be reduced?
To reduce average acceleration, we must reduce the change in velocity or increase the impact time. Helmets are one solution and designed to increase impact time.
Law of Angular acceleration ∑𝛕 = 𝑰 ∙ 𝜶
Torque = 𝑰 x (∆angular v / time) Torque x t = 𝑰 x (∆angular v / t) x t Torquext =𝑰x∆angularv Angular Impulse = Angular Momentum
Swing phase is subdivided into 3 gait events
Traditional • Acceleration • Mid swing • Deceleration
Stance phase is subdivided into 5 gait events
Traditional • Heel strike • Foot flat • Mid stance • Heel off • Toe off
What bat is easier to swing? with weight at the end or with weight on handle
When mass is closer to the axis of rotation, the easier it is to swing the bat • Bat B's weight is distributed closer to the axis of rotation, moment of inertia is lower than bat A. • A lower moment of inertia bat requires less force to rotate around a pivot point.
Terminal swing / Deceleration
When the swing limb begins to extend and ends just prior to initial contact (heel strike)
Newton's 1st law of motion
a body in motion remains in motion, or a body at rest remains at rest unless a force acts on it
Lever (bone)•
a rigid bar that rotates about an axis of rotation
energy
ability to do work (ΔE = W)
theta=arctan(opp/adj) opp=y2-y1 adj=x2-x1 θ = 𝐭𝐚𝐧−𝟏(y proximal - y distal/ x proximal - x distal )
absolute angle calc..
Rotation requires.... of the object to change the direction of linear velocity
acceleration
EMG signal is
an electrical signal associated with the contraction of a muscle
What are the three types of angular accelerations ?
angular tangential radial
CoM can be calculated using the
anthropometric table
Mathematically, absolute angles can be calculated from the endpoint coordinates by using the
arctangent (inverse tangent) function
Colinear forces
are forces that have the same line of action
To initiate walking, the body creates KE -
because of motion and the energy stored in a moving object
Shorter LoG means..
better balance and stability Adding contact points increase balance & stability
Right-Hand Thumb Rule...
curled fingers of the right-hand point in the direction of the rotation, direction of the extended thumb point to the direction of the vector Positive angles = counter-clockwise rotation Negative angles = clockwise rotation
Angular Displacement
defines the change in angular position Can be measured in degrees (°) or radians (rad) Angular displacement is a vector ∆𝜃=𝜃f −𝜃i Negative angles = clockwise rotation• Positive angles = counter-clockwise rotation
The center of mass is the point about which the body's mass is evenly ...
distributed
After passing its maximum, the object starts to move, and the ....takes over.
dynamic friction force
During walking
energy is constantly exchanged between PE and KE.
Impusle
force is not applied at an instant but over time force over time that creates movements
Frction
force that resists the sliding of two objects in contact -Always parallel to the surfaces in contact, and they oppose any motion or attempted motion.
formula for impulse
force x time
Newton's 3rd law of motion
forces act in pairs -for every action, there is an equal and opposite reaction
Coplanar forces:
forces are not in the same line but are in the same plane
External forces
forces that act on an object as a result of its interaction with the environment surrounding it -gravity, friction, normal force, etc
Internal forces
forces that act within the object or system whose motion is being investigated
