Lecture 11, General Motion - Describing Linear and Angular Movements Flashcards
Forms of Motion
most examples of human movement are general motion - but separating motion into its individual components makes it easier to analyze the action (the speed of the action translates well to the the speed of the translation - the relationship between linear and angular)
- we could analyze the rotation at the joints - the movement at the hip or shoulder
- we could analyze the translation of the limbs - the movement at the legs or arm
- even time your leg rotates you also take a step and translate
- when your arms swing they swing at a specific pace as there is normally relationship between for far your rotate and how far your translate
- to produce linear acceleration you need force - to produce angular acceleration you need torque
General Motion (ball)
the ball spins (rotation) as it travels through the air (translation)
there is a relationship between the two forms of motion
- the more the ball spins the further the ball travels
- the faster the ball rotates, the faster the ball translates
- the faster the rotation on the ball the faster it is going to translate
- if we know one we we can calculate the other (angular and linear are not the same thing as there are dependent on a critical factor)
Relating Linear and Angular Variables (shoulder, elbow, arm)
imagine this line segment represents your arm
the axis of rotation (origin of motion) is at your shoulder
as your arm swings back and forth the elbow changes position (or translates)
as your arm swings back and forth the hand changes position (or translates) - how far your hand translates everytime your shoulder rotates therefore the radius of rotation would be the linear distance between the axis of rotation (shoulder) and point of interest (hand)
- radius of rotation is a linear distance between two points (between axis of rotation (origin of where movement is occurring) and distance to something of interest (an object) - can measure in metres where axis of rotation is shoulder and object can be hand or elbow for example (as the hand and elbow move)
- the radius of rotation allows you to convert linear values into angular values
Relating Linear and Angular Variables (radius of rotation)
- the linear change in position on a rotating object will be different at each point along the system (how far a ball rotates/translates and how fast it rotates/translates - there are not always the same thing but how big or small they are depends on the radius of rotation)
- the amount of change will be dependent upon the distance between the axis of rotation and the point of interest on a system (r), the radius of rotation
- the hand will travel further and faster because of radius of rotation being bigger as compared to the elbow
- when a system rotates about an axis:
◦ how far a point on that system translates.. l = rΦ (linear path of travel is equal to the total amount of rotation when you take into account radius of rotation) - r is found being multiplied to the angular value
◦ how fast a point on that system translates.. v = rω (can represent how fast it rotates when taking into account radius of rotation)
◦ the size of dynamic change.. a = rα (can equate them together when angular is with r)
◦ …is dependent on the radius of rotation - whenever we equate linear and angular changes together we have to taken into account the total for both (angular and linear movement) so we cannot take displacement into account rather distance (do not use displacement in general kinematic
Relating Linear and Angular Variables (why is there is a mixture or scalar and vector quantities used?)
why do we use linear and distance (scalar quantity), but then use velocity and acceleration (vector quantities)?
a radian is a ratio of the distance around the circle to the radius of the circle
measuring displacement, a change in position, would underestimate how far a system has moved
- arc length, line in and out of the centre creates the radian where angle is 57.3 (is you are measuring displacement you are ignoring some of the movement as you put the line through the middle as it is only change in position and thus we take into account total movement to include the arc length and to capture the entire movement)
What is the radius of rotation?
the linear distance from the axis of rotation to a point of interest on the system
The Radius of Rotation and Movement - why does a batter “choke up” (slide their hands away from the handle) on a bat?
- you can either be fast or accurate (trade-off)
- choking up decreases the radius of rotation - decreases the bat speed, giving the batter more control (holding it higher) - swing as fast you possibly can but the bat will not get as far as so linear velocity slows down giving the batter more control
- choking down increases the radius of rotation - the bat head travels faster, so the ball will travel faster (magnifying the movement) - by increasing radius of rotation the linear velocity will be faster so the ball will travel further (create a bigger linear affect)
Linear Movement of an Angular Body (tangential)
the ball spins in a clockwise direction
when the ball spaced on the ground, the angular motion will create linear movement
which way will the ball translate? to the left? or to the right?
- an angular movement created linear movement (a rolling object can give rise to linear change but if you just sliding an object there is no angular change)
- a spinning object hitting the ground will roll
- tangent is line that touches the curve but does not cross it (reflects the direction of linear change on a rotating object - tangent line) - the direction of the linear movement is on a tangent to the movement object
- tangent and linear mean the same thing
- vt = r ω (tangential means the object was rotating and as a cause is translating)
- at = rα (tangential acceleration but it is still linear, there is just rotational component that gives rise to linear movement) rotating object is speeding up or slowing down where we have linear acceleration on the rotating object - linear is equal to angular when radius of rotation is taken into account
- the subscript means tangential
- the linear value of a point on a rotating rigid object at a distance from the axis of rotation represents the tangential quantity of that poi
Linear Acceleration of an Angular Body - can an object moving around a curve at constant speed be accelerating?
while the magnitude is not changing but the direction is so a force must be present to create the change (forces create, change or prevent moment)
- velocity is a vector - a quantity having direction (sign) and magnitude (number)
- if there is a change in either component, then velocity is changing (if direction is changing, then there must be acceleration) - does not impact the speed but impacts the direction
Linear Acceleration of an Angular Body (centripetal/radial acceleration)
a point on an object spinning at a constant angular velocity is constantly changing direction and is experiencing linear acceleration
- centripetal (or radial) acceleration is present when an object changes direction - causes changes in direction which are measured by centripetal acceleration (radial and centripetal can be used interchangeably)
- the force that cause centripetal acceleration to occur is directed towards the axis of rotation
- ar = v2/r (measure the velocity at a given point in time and how far you are from curve) - measure how far away you are from the curve and how fast your are moving
- radial force gives rise to radial acceleration
- where are you in your path of travel with respect to the axis of rotation
- the tighter the curve the more chance of not making it (more force you need)
- if you really want to go fast around turn you seem to go wider around the turn
- in order to create radial acceleration and change in direction you need force - so the bigger the radial acceleration the more radial force is present (more force required to make a sharper turn or a faster turn)
- when you need to go straight there is reaction force but when you want to go to the side along a curve you need additional force to go sideways (radial force) which gives rise to centripetal acceleration - need to have that propels you forward and and sideways (the more force you put into one the less you have to put into the other) - LINEAR CONCEPT (the change of direction in a linear object)
Centripetal (Radial) Acceleration
the linear acceleration directed toward the axis of rotation
ar = v2/r
- ar increases as radius of rotation decreases - more force would be required to make a sharper turn
- ar increases as velocity increases, more force would be required to make a turn faster
- the faster you want to go the wider the curve and the more tight the curve the more force required
Linear Acceleration of an Angular Body - when competing in a 400m race is there one lane that offers a biomechanical advantage?
- ar = v2/r (there is not much of a curve so you can put more force to propel urself to the side rather than sideways for lane 8 at the end)
- have to make tightest turn in lane 1 and widest in lane 8
- need to put so much effort to push yourself around the curve for lane 1
- there is also a psychological advantage of wanting to chase someone as someone in lane 8 cannot see their competition
Linear Acceleration of an Angular Body (total acceleration)
- the total acceleration of a system is the vector sum of the tangential acceleration and centripetal acceleration
- have to consider how far your rotate and if that rotation is changing AND are you going along a straight line or some curved path
- radial acceleration is looked at from an outside point to the centre
- the total acceleration looks at is this object traveling along a straight path or curved path and is this doing it at the same rate or a changing rate (can attain this value through phythagorean theorm)
Assessing General Body Movements
- according to the formulas of general motion there should be a positive linear relationship between linear and angular variables
◦ if the linear variable increases the angular variable increases accordingly
◦ if the linear variable decreases the angular variable decreases accordingly - this, however, is not the case when it comes to internal movements in the human body
- there is a non-linear relationship between linear and angular variables when it comes to movements inside the human body
Assessing General Body Movements - diagram
- changes that exist in the muscle are not exactly the same that exact at the joint
- nonlinear relationship between velocity and angular velocity
- the red line represents the change at the elbow (angle) - as you flex the joint closes at fairly constant rate
- when the joint starts moving the muscle starts moving - the muscle starts moving really fast to keep up with the joint
- muscle reaches peak and then starts slowing down, so it is a nonlinear relationship as what is happening at the muscle is not happening at the joint
- you have multiple muscles at the joint all of which work at different times as they all have preferred lengths - since we have different mechanical properties and multiple muscles acting at the joint it creates a nonlinear relationship between linear and angular changes inside of the body
