Angular Kinematics Flashcards
What is kinematics?
- description of motion
- geometry of motion
- “what” happened
What is angular kinematics?
- motion of a body (person or object) or body part around a fixed axis through an angle of X number of degrees
- rotation (spinning, swinging, twisting etc.)
Define relative angle.
- the angle formed between two adjacent body segments
- anatomical reference postion: relative angles are zero
Define absolute angle.
angular orientation of a single body segment with respect to a fixed line of reference (vertical and horizontal reference)
Define angular distance.
sum of angular changes undergone by rotating body
Define angular displacement.
- assessed as difference of initial and final positions
- counter-clockwise (+) or clockwise (-)
- right hand rule
What is the right hand rule?
- point the thumb of your right hand towards the positive linear direction along the axis of rotation
- the direction in which your fingers curl is the positive direction of rotation
What are the 3 ways to measure angular distance?
- revolutions
- degrees
- radians
1 rev = ______ degrees = ___ radians
360 degrees = 2π
What is a degree?
1/360th of a revolution
When L=r in calculating radians, this means what?
1 radian
What is a radian?
the angle which includes the arc of a circle equal to the radius of the same circle
1 radian = ___ degrees
57.3 degrees
How do you convert from degrees to radians?
- multiply by π/180
- divide by 57.3
How do you convert from radians to degrees?
- multiply by 180/π
- multiply by 57.3
How do we measure angular displacement?
- by calculating the number of radians
Describe the relationship between linear and angular displacement.
- the greater the distance of a given point on a rotating body from the axis of rotation, the greater the linear displacement of that point
- L = rθ
How do the formulas for linear velocity and angular velocity differ?
- linear: v = d/t
- angular: ω = θ/t
Describe the formula for angular speed and how it differs from the formula for angular velocity.
- angular speed = angular distance/change in time
- angular velocity = angular displacement/change in time
What are the units for angular speed?
deg/s, rad/s, rpm
Describe the relationship between linear and angular velocity.
- an object travelling in a circular path will follow a path that is a straight line when released (spiderman)
- the new path will be at a tangent to the radius of rotation (trebuchet)
What is tangential velocity (v T)?
the velocity of the released object that was travelling in a circular path becomes linear velocity and changes from ω to v
Describe the relationship between ω and v. Give examples.
- longer radius = greater linear velocity
- if all things are equal (angular velocities remain constant)
- ex. longer levers increase velocity (given equivalent ω)
- ex. baseball batter extends his arms before contact
What is tangential acceleration?
the component of linear acceleration tangent to the circular path of a point on a rotating object
In an object with constant ω, is there still acceleration?
yes. Linear acceleration: speeds up, slows down, or changes direction
Describe linear acceleration that occurs in an object with constant ω.
- towards the centre
- centripetal (radial acceleration)
- force that causes this is centripetal force
- equal/opposite force = centrifugal force
The _____ the distance of a given point on a rotating body from the axis of rotation, the
_____ the linear displacement of that point (assuming the same angular displacement)
greater, greater
What is a tangent?
- line that just touches the arc created by a point on a rotating body
- perpendicular to the radius of the arc at that point
longer vs shorter radius, ω equal for both, _____ radius will have greater vT
longer
longer vs shorter radius, vT equal for both, _____ radius will have greater ω
shorter
