Angular Motion
Learning Outcomes
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All pupils will be able to remember
and understand the theory behind
projectile motion.
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Most pupils will be able to apply the
theory of projectile motion and
angular motion to sporting
examples.
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Some pupils will be able to explain,
evaluate and create links between
sporting movements relating to
angular motion
Starter Activity
 Answer
motion.
exam question on projectile
Homework
 Complete
Pink booklet section on
Mechanics of movement
 Complete exam questions on angular
motion.
 Work on coursework (coursework club
Tues 3.30pm 16R)
Rotational movements
 Look
at diagram and label, draw on
whiteboard:
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1. names of the axis
2. angular movement at the axis
3. give sporting examples
Angular motion
Angular motion is movement around a fixed
point or axis, e.g. a somersault.
Remember angular motion occurs when a
force is applied outside the centre of mass
(eccentric force).
Centre of Mass
The centre of mass is very simply the point of
balance.
Torque (moment of force)
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Torques are forces that produce rotation
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Torque(Nm) = size of force(f) x Moment arm or
distance from
the fulcrum (d)
F
d
Principle of moment
 If
both clockwise and anticlockwise
motion applied then there is NET ZERO
TORQUE (balanced)
 E.g. isometric contraction (pike)
Label and explain what torque is
Torque
Torque
F
d
Newtons analogue Laws
 N1
– remain at constant angular velocity
(continue to turn) until an external torque
acts
 N2 – angular acceleration is proportional
to torque and in that direction
 N3 – an object will always apply a
reaction torque which is proportional in
size but opposite in direction.
Angular analogues of
Newton’s Laws
Newton’s
Laws
Law of
conservation
Law of
acceleration
(rotation)
Law of
reaction
Application
a rotating body will continue in
an ice skater spinning will
its state of angular motion unless
an external force (torque) is
exerted upon it.
the rate of change of angular
momentum of a body is
proportional to the force
(torque) causing it and the
change that takes place in the
direction in which the force
(torque) acts
leaning forwards from a diving
board will create
when a force (torque) is applied
by one body to another,
the second body will exert an
equal and opposite force
(torque) on the other body
in a dive, changing position from a
tight tuck to a lay out position, the
diver rotates the trunk back
(extends the trunk). The reaction is
for the lower body to rotate the
opposite direction (extension at the
hips).
Angular analogues of
Newton’s Laws
Newton’s Laws
Law of
conservation
Law of
acceleration
(rotation)
Application
a rotating body will continue in
its state of angular motion
unless an external force
(torque) is exerted upon it.
an ice skater spinning will continue
to spin until they land. Here the
ground exerts an external force
(torque), which changes their state
of angular momentum
the rate of change of angular
momentum of a body is
proportional to the force
(torque) causing it and the
change that takes place in the
direction in which the force
(torque) acts
leaning forwards from a diving
board will create more angular
momentum than standing straight.
when a force (torque) is
Law of reaction applied by one body to
another, the second body
will exert an equal and
opposite force (torque) on the
other body
in a dive, changing position from a
tight tuck to a lay out position, the
diver rotates the trunk back
(extends the trunk). The reaction is
for the lower body to rotate the
opposite direction (extension at the
hips).
Angular momentum
 Quantity
of rotational motion a body
possesses
 AM = angular velocity x moment of inertia
 Angular
velocity – rate of turn/spin
 Moment of Inertia – the distribution of
mass around the axis of rotation
Angular momentum
 AM
is conserved during flight
 Angular
velocity and moment of inertia
are inversely proportional, if moment of
inertia increases angular velocity
decreases and vice versa.
 Control
angular velocity by changing
moment of inertia
Relationship
Changing Moment of Inertia
 http://www.youtube.com/watch?v=YqQz
W2dFI9s
 http://www.youtube.com/watch?v=KXz6
QzxxjZE
 Compare
the straight back and tuck
back somersaults
 Apply this also to a swimmer in front crawl
Changing Moment of Inertia
 The
tucked shape is faster because the
mass of the trampolinist is closer to the
rotational axis
Changing Moment of Inertia
 The
same can be said for swimmers in
front crawl; after the propulsive phase,
the arm leaves the water and flexes at
the elbow
 This reduces the moment of inertia and
helps increase the speed of the recovery
phase
Conservation of Angular
momentum

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Task: apply this to a figure skater performing
multiple spins.
Ice is a friction free surface so there is no
resistance to movement. The skater can
manipulate their moment of inertia to increase or
decreases the speed of the spin.
Large
moment of
inertia and
large angular
momentum –
rotation is slow
Reduced
moment of
inertia and
increased
angular
momentum –
rotation is fast
Exam questions

(c) Figure 1 shows a diver performing a
tucked backward one-and-one–half
somersault.

Use figure 1 to explain why performing this
dive in a tucked position is easier than
performing it in an extended position.
(5 marks)
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(c)
1 (In air / during flight) angular momentum remains constant (may
be shown as straight line on graph);
2 Because there are no net external forces acting;
3 Angular momentum = angular velocity x moment of inertia;
4 A change in moment of inertia results in a change in angular
velolcity
(may be shown on graph);
5 Tucked somersault has smaller moment of inertia than extended;
6 Hence rotation / angular velocity is quicker in tucked somersault;
7 The problem of somersaulting is the need to complete the
movement quickly / lack of time – hence tucked somersault easier
to do.
Any 5 for 5 marks
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
Figure 2 shows an ice-skater performing part
of their routine.
(b) Using figure 2 explain the mechanical
principles that allow spinning ice-skaters to
adjust their rate of spin.
(6 marks)
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(b)
1. Ice may be regarded as a friction free surface/friction is
negligible;
2. During spins angular momentum remains constant;
3. Angular momentum is the quantity of rotation;
4. Angular momentum = angular velocity x moment of
inertia;
5. Angular velocity = rate of spin/how fast skater spins;
6. Moment of inertia = distribution/spread of mass around
axis;
7. Changing/reducing moment of inertia affects/increases
angular velocity;
8. Skater brings arms into body allowing rate of spin to
increase;
(Accept annotated diagrams/graphs) 6 marks
Plenary Activity
 How
does a high diver use a knowledge
of angular momentum to control a triple
somersault dive?
(14 marks)