Angular kinetics Flashcards
Definition of kinematics?
The branch of mechanics concerned with the motion of objects without reference to the forces which cause the motion
Definition of kinetics?
The branch of mechanics that deals with the actions of forces in producing or changing the motion of masses
How to convert radians into degrees?
360 degrees = 2 pi radians
Symbol for angular velocity?
Omega - curly w
Symbol for angular acceleration?
Alpha
How to calculate linear displacement from angular displacement (formula)
theta x radius
where theta = angular displacement measured in radians
How is 1 radian defined
The arc with length equal to the radius
How to calculate linear speed (tangential velocity) from angular velocity (formula)?
omega x radius
where omega = angular velocity measured in radians
What direction does centripetal force act in?
What does centripetal mean?
Inwards along the radius
“Centre seeking”
What are the two formulas for calculating centripetal acceleration?
= tangential velocity^2 / radius
= angular velocity^2 x radius
Impulse - what is the:
formula?
units?
Force x time
Ns
Momentum - what is the:
formula?
units?
Mass x velocity
kg.m.s-1
What is another name for torque?
Moment
Torque - what is the:
formula?
units?
Force x perpendicular distance to axis of rotation
N.m
Torque impulse - what is the:
formula?
units?
Torque x time
N.m.s
Angular momentum - what is the:
formula?
units?
Moment of inertia x angular velocity
kg.m2.s-1
Moment of inertia - what is the:
formula?
units?
Mass x (radius of rotation)2
kg.m2
What is the definition/formula for torque?
Force x the torque/moment arm
“The tendency of a force to cause a rotation about a specific axis”
Not a force but the effect of a force in creating a rotation
What is the definition of torque/moment arm?
The shortest distance between the line of action and the centre of rotation
What is the definition of moment of inertia?
The resistance of an object to change in angular motion (and is dependent on the axis of rotation)
What is an eccentric force?
A force not passing through the centre of mass
What is a force couple?
give 2 examples
2 forces of equal magnitude acting on a body at a distance apart from each other
- gymnast executing a twist about longitudinal axis (applies backwards force with one foot and a forwards force with the) other
- use of thumb and forefinger to screw open a jar lid
What is the formula linking torque to angular acceleration?
Torque = moment of inertia x angular acceleration
Torque = mass x radius [of gyration]2 x mass
What is the formula linking the angular acceleration of linked objects to the torque acting on them?
Sum of the torques acting on the linked objects
= angular acceleration x sum of moments of inertia
Define the radius of gyration
The distance between the axis of rotation and an imaginary point on the segment where all of its mass would be considered to act if it had the same moment of inertia as the segment
Explain (in words) the parallel axis theorem
The moment of inertia around the whole-body centre of mass is equal to the sum of all of the individual segment movements of inertia about their own centre of mass plus their individual masses multiplied by the squared distances between their centres of mass and the whole body centre of mass
Explain the parallel access theorem (formula)
Moment of inertia (whole body)
=
Sum for all segments ( segment moment of inertia + segment mass x distance between segment and whole body centre of mass ^ 2)
What is the formula for moment of inertia of a segment about the transverse/ mediolateral axis of the segment?
mass x radius of gyration around transverse/mediolateral axis ^ 2
What are two formulae for angular momentum
1 with respect to moment of inertia
1 with respect to radius of gyration
Angular momentum
= moment of inertia x angular velocity
= mass x radius of gyration^2 x angular velocity
What are the units of angular momentum?
kg.m2.s-1
Radians do not appear in this as they are dimensionless
What rule denotes the direction of angular momentum?
Right hand rule
Perpendicular to plane of motion
Anti-clockwise and upwards is usually denoted as positive
What is the angular equivalent of Newton’s first law of motion?
A body will continue in a state of uniform angular motion unless acted on by an external torque or moment
What is the angular equivalent of Newton’s second law of motion?
An external torque or moment produces an angular acceleration of a body that is proportional to and in the direction of the torque and inversely proportional to the moment of inertia
What is the angular equivalent of Newton’s third la of motion?
For every torque or moment exerted by one body on another body there is an equal and opposite torque or moment exerted by the latter body on the former
What is the principle of conservation of angular momentum?
If no external torque is applied to a system, angular momentum remains unchanged
Explain the principle of moments
For a rigid body in a state of equilibrium the sum of moments about any point must equal zero
What is the formula for the angular equivalent of Newton’s second law?
Torque = moment of inertia x angular acceleration
What is the formula relating torque to angular momentum?
Torque x (delta) time = (delta) angular momentum
From which of Newton’s laws is the principle of conservation of angular momentum derived?
Newton’s first law
How does gravity relate to angular momentum during flight?
When gravity is the only external force acting on an object angular momentum (at take-off) remains constant for the duration of the flight
What is the terminology for a combination of rotation and translation (linear motion)
General motion
What is an example of how angular momentum about one axis may be transferred to another?
Full twisting one and a half somersault
What is an example of a rotation initiated even when total body angular momentum is nil?
Cat twisting in order to land
What is the formula for calculating the angular momentum of a [segment] about total body centre of mass?
Equal to:
H(Local) - angular momentum of segment about its own centre of mass
+
H(Remote) - angular momentum of segment about total body centre of mass
How is the moment of inertia of a segment of a rotating person calculated?
Moment of inertia of the segment around its own centre of mass + mass of segment x distance from the COM of segment to AXIS OF ROTATION squared
