1. Torques and moments of force

2.  Define Torque and identify the factors
affecting torque
 Differentiate between the different classes of
levers.
 Demonstrate the ability to calculate torques
and muscular torques

3.  A torque is the turning effect that is produced by
a force
◦ Can also be known as a moment of force.
◦ or simply a moment.

4.  Lay a book flat on a table.
◦ Where does the books centre of gravity lay.
 Apply a force through the books top edge
just off the books centre of gravity
◦ What happened?
 Repeat a number of times, each time, strike
the book so the line of action is farther away
from the centre of gravity
◦ What happened?

5.  What factors affect
torque?
◦ Distance between the line
of action of action and the
axis of rotation
◦ Size of the force
 So we can define Torque as
◦ The turning effect produced by a force and is equal
to the product of the magnitude of the force and
the distance between the line of action of the force
and the axis of rotation to the object

6.  The distance between the line of action of the force
and the axis of rotation (a) is the perpendicular
distance between the line of action of the force and
a line parallel to it that passes through the axis of
rotation.
 This can be simply
defined as the moment
arm, and can be seen in
the diagram as r

7.  Mathematically, torque can be defined as:
◦ T = F x r
◦ Where
◦ T = torque (Nm)
◦ F = Force (N)
◦ R = moment arm (m)
 Note
 Torque is a vector quantity, You must specify a direction
(+) (-)Counter clockwise Clockwise

8.  The width of a door is 80 cm. If it is opened by
applying a force of 20 N at its edge (away from the
hinges), calculate the torque produced which
causes the door to open.
 Solution :
Length of lever arm = 40 cm = 0.40 m (since distance
between axis of rotation and line of action of
force is 40 cm)
Force applied = 20 N
T = F x r
= 20 x 0.8
= 16 Nm (8 Newton meter)
Answer : Torque = 16 Nm

9.  In the previous question, if the handle of the door
is situated 20 cm from the edge, and we know the
torque required to open the door is 16Nm, What is
the force applied through the handle to open the
door?
 Solution :
Length of lever arm = 80 cm - 20 cm = 60 cm =
0.60m
Torque = F x r
16N = F x 0.60
 F = 16/0.6

Answer : Force = 26.7 N

10.  A lever is a rigid object that is used with an axis to
either multiply the mechanical force (effort) or
resistance force (load) applied to it.
 There are 3 components to a lever
 Axis (pivot or fulcrum)
 Resistance load (weight)
 Force (effort)

11. The fulcrum is located between the
applied force and the load
The load is situated between the
fulcrum and the force
The force is applied between
the fulcrum and the load

13.  Muscles create the torques that turn our limbs.
When a muscles contracts it pulls on its points of
attachment, along a line of action (or line of pull)
 Because the line
of action of the
muscle force is
some distance
from the joint axis
(fulcrum) a
moment arm exits
(r)

14.  Consider how the moment arm (r) changes as the
arm flexes
What affect does that have
on the biceps brachii’s
ability to create a torque
about the elbow joint?

15.  As the forearm is flexed and extended, the
moment arm changes.
◦ The moment arm is biggest when the elbow is at 90
degrees, and gets smaller as it is flexed and extended away
from this position.
 A similar situation exists
for most of our muscles
and the joints they cross.
 Explains why our muscles
are apparently stronger in
some joint positions than
others

16.  As muscle attachments are much closer to the joint
axis than the load, muscles have to create large
forces just to hold a static position.
 You are holding a 20kg dumbbell in an isometric
position with your elbow at 90 degrees. The
moment arm of the dumbbell is 30cm about the
elbow joint axis.
◦ What torque is created by this dumbbell about your joint
axis?
 T = F x r
 T = 200 N x 0.3
 T = 600 Nm

17.  To hold the dumbbell in this isometric position
your elbow flexor muscles, must create a clockwise
torque equal to the counter clockwise torque
created by the dumbbell.
 If the muscle attachment is 5cm from the joint
axis, what force must they pull at to keep the
dumbbell in this position?
 T = F x r
 600 Nm = F x 0.05m
 F = 600 / 0.05
 F = 1200N

18.  The Achilles tendon inserts on the calcaneus (heel
bone) at a distance of 8 cm from the axis of the
ankle joint. If the force generated by the muscles
attached to the Achilles tendon is 3000N, and the
moment arm of the force about the ankle joint is
5cm, what torque is created by these muscles
about the ankle joint?

19.  An athlete is doing a knee extension exercise
using a 100 N dumbbell. She holds her leg
so that the horizontal distance from her knee
joint to the dumbbell is 30cm.
◦ (a) For this position what torque is created by the
dumbbell about her knee joint axis?
◦ (b) If the moment arm of the knee extensor muscles
is 4cm about the knee joint axis, what amount of
force must the muscles produce to hold the leg in
the position described.

20.  An athlete is attempting to lift 15kg. The
moment arm of the this weight about his
elbow joint s 25cm. The force created by the
elbow flexor muscles is 2000 N. The moment
arm of the elbow flexor muscles is 2cm.
◦ Is the athlete able to left the weight with this
amount of force in his flexor muscles?

21.  We can define Torque and identify the factors
affecting torque
 We can differentiate between the different
classes of levers.
 We Can demonstrate the ability to calculate
torques and muscular torques