angular motion Flashcards
what is angular motion
it refers to rotation and involves turning around an axis
angular motion can be a whole body or a part of a body like arms or legs
examples of angular motion for a part of a body
throwing a discuss, arms and legs whist running, forehand in tennis
how do we create a turning force
we apply the force eccentrically
eccentric forces create more torque
angular motion occurs as a result of…
torque
what is torque
it is a turning force that causes an object to rotate around its axis
often called a moment
a formula that involves torque
moment of force=
moment of force (torque-newton meters) = force (N) x perpendicular distance from fulcrum (m)
if you increase the size of the force it increases torque what happens to angular motion
it is increased
how can torque be changed to have different effects on angular motion
if it is applied closer to or further away from the axis of movement
what affect does perpendicular distance from fulcrum (pivotal point) have on torque
the greater the distance the the more we multiply by and so the greater the torque
what is newtons first law in relation to AM
a rotating body will continue to turn about its axis of rotation with constant angular momentum unless an external rotational force (torque) is exerted upon it
what is newtons first law in relation to AM applied to a figure skater
spinning in flight they will continue to spin until they land and an external force is applied onto their skates this will change and slow their angular momentum, this force will be friction
what is newtons 2nd law in relation to AM
the rate of change of angular momentum of a body is proportional to the force (torque) causing it and the change takes place in the direction in which the force (torque) acts
the greater torque (turning force) exerted the faster the rotation
what does the moment of force =
(2nd)
moment of force (torque-newton meters)= force (newtons) X perpendicular distance from fulcrum (pivotal point) (m)
apply newtons 2nd law in relation to AM for lacrosse sticks
with a longer stick (defense) there is a longer perpendicular distance from the fulcrum so you can propel the ball with the most force
shortest stick (attack/midfield) there is a shorter perpendicular distance from the fulcrum so it allows more control
what is newtons 3rd law in relation to AM
when a force (torque) is applied by one body to another the second body will exert an equal and opposite force (torque)
apply newtons 3rd law in relation to AM for a tennis lpayer
a tennis player applies a downwards slice action on the ball it will rotate (spin) to replicate the amount of torque provided
what is angular displacement
the smallest change in angle between the starting and finishing point of rotation
the change in the angle as an object moves in a circular path
how many degrees is 1 radian
57.3 degrees
is angular displacement a scalar or vector
vector
how many degrees is 1 radian
57.3 degrees
how many radians/the angular displacement of 360 degrees (inc working out)
360 degrees is not zero displacement
360/57.3=6.28 radians
formula for angular displacement
angular displacement=angular velocity x time taken
what is angular velocity
rotational speed of the object, rate of change of angular displacement
ms: AV is the rate of rotation of a body around its axes of rotation.
is angular velocity a scalar or vector and why
vector because it refers to the angular displacement that is covered in a certain time
formula for angular velocity
angular velocity= angular displacement (rad)/time taken
a performer spins from one position to another on the parallel bars, spinning 110 degrees from point x to y in 0.5 secs, what is the angular velocity
AD= 110/57.3 = 1.9 rads displacement
1.9/0.5 = 3.8 rad/s
what is moment of inertia
the resistance of a body to angular motion (spin)
reluctance to change its current state of rotational motion
level of force that has to be applied in order to maintain inertia
ms: MOI is the bodys reluctance to rotation/to alter rate of rotation
what can the moment of inertia depend on
the mass of the body and the distribution of mass around the axis of rotation
both can be manipulated
how can mass affect the moment of inertia
the greater the mass the greater the resistance to change and therefore the greater moment of inertia
how can the distribution of mass affect the moment of inertia
the closer the mass is to the axis of rotation the easier it is to rotate, this is because the moment of inertia is lower, increasing the distribution of mass away from the axis of rotation will increase the reluctance to rotate (increasing moment of inertia)
formula for moment of inertia
body mass x distance from axis of rotation ^2
kg m^2
what is angular momentum
the amount of angular motion of an object when turning
quantity of rotation
what is the conservation of angular momentum
angular momentum is conserved when a body is in flight and there is an inversely proportional relationship between angular velocity and moment of inertia
it stays constant unless external force (torque) is applied (n1st law)
ms: the principle of COAM states that AM remains constant, if MOI decreases, AV increases and vice versa
formula for angular momentum
moment of inertia (kg m^2) x angular velocity rads/s
kg m^2 rads/sec
what is angular acceleration
the rate of change of angular velocity
formula for angular acceleration
change in AV (rad/s)/time taken ^2
rad/s^2
to increase angular velocity what do you do
increase the moment of inertia
distributing the mass further away from the centre of gravity
spread out the body
to decrease angular velocity what do you do
decrease moment of inertia
distributing the mass closer to the centre of gravity
tuck the body in
apply the moment of inertia to a sprinter
driving leg (extending) is far from the hip and therefore has a large moment of inertia
the recovery leg that flexes allows its mass to travel closer to the axis of rotation and therefore moves quicker as it reduces to the moment of inertia
gymnasts have to change the position of their body when performing a somersault during a floor routine
explain how a gymnast alters their angular velocity by changing their moment of inertia (4)
angular momentum= moment of inertia x angular velocity (during rotation)
angular momentum remains constant/conservation of angular
momentum.
to slow down (rotation) gymnast increases moment of inertia.
achieved by extending body/opening out/or equivalent
to increase speed of rotation gymnast decreases moment of inertia
achieved by tucking/bringing arms towards rotational axis
explain how a gymnast can alter the speed of rotation during flight (8 marks)
changing shape of the body will causes a change in speed.
change in moi leads to change in av/speed of rotation.
angular mom remains constant
angular mom=moi x av
av is speed of rotation
moi- distribution of mass around axis/reluctance of the body to move.
to slow down rotation increase moi done by extending out body.
to increase speed decreases moi achieved by tucking the body in.
draw diagram
analyse how newtons laws of angular motion can account for the figure skaters speed of rotation throughout the movement (3)
1st law…
the ice skater will rotate with constant angular momentum in the air if there is no external torque/rotational force slowing them down until they land back on the ice
analyse how newtons laws of angular motion can account for the figure skaters speed of rotation throughout the movement (3)
2nd law…
the more torque/rotational force the skater pushes off the ice the faster they will rotate allowing them to complete their rotations before returning to the ice
analyse how newtons laws of angular motion can account for the figure skaters speed of rotation throughout the movement (3)
3rd law…
when the rotating skater lands back on the ice the torque they apply to the ice is returned to them slowing them down
at take off the skater will apply torque to the ice which will generate torque in the opposite direction causing the skater to rotate.
analyse how the gymnast makes use of the principle of conservation of angular momentum when performing to a front tuck somersault. refer to the graph above in the answer (graph being that on COAM) (15)
AO1:
AM is the quantity of rotation a body possesses and is a product of MOI x AV > = AM
MOI is the bodys reluctance to rotation/to alter rate of rotation
AV is the rate of rotation of a body around its axes of rotation.
AA is the rate of change of AV.
the principle of COAM states that AM remains constant, if MOI decreases, AV increases and vice versa
analyse how the gymnast makes use of the principle of conservation of angular momentum when performing to a front tuck somersault. refer to the graph above in the answer (graph being that on COAM) (15)
AO2:
MOI is high at the start and the end of the somersault but low in the middle of the movement.
AV is low at both the start and end but high in the middle. start and end/go into/out of somersault, slowing the rate of rotation
AA is occurring as the performer begins the somersault and angular deceleration occurs as they complete the somersault.
AM remains constant
analyse how the gymnast makes use of the principle of conservation of angular momentum when performing to a front tuck somersault. refer to the graph above in the answer (graph being that on COAM) (15)
AO3:
gymnast is in an open position initially = large MOI = low AV
gets into tucked position > mass is distributed closer to their COM = reduced MOI, increased AV
AA as a result of reduced MOI and increased AV > full rotation to occur quickly > time to land safely
opens out from tuck = MOI increases, mass is further from COM, AV decreases (AD) > slow down prior to land = control maintained.
AM remains constant as they manipulate their body to reduce MOI and increase AV whilst maintaining AM
explain newtons laws of motion in relation to the dancer spinning and how the dancer can alter her rate of spin (15) newtons first law 1, 2, 3
AO1: states that a body will continue to turn about its axis of rotation with constant angular momentum unless a force is exerted upon it
AO2: therefore dancer will continue to spin with constant angular mom unless an external force acts on her
AO3: this is known as the principle of conservation of AM. the dancer can alter her rate of spin by moving her limbs either closer or further away from the axis of rotation there fore to increase her rate of spin she will need to bring her arms close to her body, without this ability she will be unable to control the movement.
if she as failed to warm up appropriately she will not be unable to achieve the most efficient position, making the spin more difficult to perform with a reduction in potential o2 delivery due to lack of suitable warm up she will fatigue more quickly reducing her ability to control spin.
