Download Angular Kinetics I

Angular Kinetics I
KIN 335 Spring 2005
What you should know
• Definition of torque (including moment arm)
• Equilibrium (static vs. dynamic equilibrium) Î
Applying the equilibrium equation
• Center of gravity vs. Center of mass
• CG calculation
• CG and Performance
• CG and Stability
What are torques?
• Torques cause changes in _________ motion.
• Movements of our limbs at joints are controlled by
the torques produced by muscles. Î Muscles
create _________ about joints, and these torques
control and cause the movements of the limbs and
the entire body.
• Definition
– Turning effect produced by a force (________ force)
– A torque is an influence which tends to change the
__________ motion of an object.
– _______________
Mechanical Definition of Torque
• Turning effect due to applied force (eccentric
force)
• Torque (T) = __________
– r : moment arm (= _______________ distance from the
axis of rotation)
– F : applied force
• Torque is proportional to ‘moment arm’(r) and
‘force’ (F)
• Finding out the moment arm?
• Unit : ______ or ft⋅lb
Q)
75°
5 cm
F
Equilibrium
• When all the forces and all the torques which act
upon an object are balanced
Î Equilibrium state
ΣF = 0 (applied net force = zero) and
ΣT = 0 (applied net torque = zero)
• Static equilibrium
– If an object is at rest and in stationary position
• Dynamic equilirium
– If an object is moving at constant velocity.
Muscle force estimate using
equilibrium equations
F =?
75°
F =?
15°
5 cm
The length of forearm is 45 cm
W = 15 kg
Q1 (chap 8) The Achilles tendon inserts on the calcaneus (the
heel bone) at a distance of 8 cm from the axis of the ankle
joint. If the force generated by the muscle attached to the
Achilles tendon is 3000 N and the moment arm of this force
about the ankle joint axis is 5 cm, what torque is created by
these muscles about the ankle joint?
Q3 (Chap 8) A weight lifter is attempting to lift 150 N. The
moment arm of the weight about her elbow joint is 25 cm. The
force created by the elbow flexor muscles id 2000 N. The moment
arm of the elbow flexor muscles id 2 cm. Is the athlete able to lift
the weight with this amount of force in her flexor muscles?
What is Center of Gravity(CG)?
• The terms "center of mass“(CM) and "center of
gravity“(CM) are used synonymously in a uniform gravity
field to represent the unique point in an object or system
which can be used to describe the system's response to
external forces and torques.
• Center of gravity
– that point in a body or system around which its mass or weight is
evenly distributed or balanced and through which the force of
gravity acts
• Center of mass
– The point in a body or system of bodies at which, for certain
purposes, the entire mass may be assumed to be concentrated: for
bodies near the earth, this coincides with the center of gravity
• Why important? When interpreting and applying Newton’s
laws of motion, it is the center of gravity of a body whose
motions are ruled by these laws.
How to locate CG of human body
•
Segmental Method
– The concept of the center of mass is that of
_________ of the masses factored by their
distances from a reference point.
– In the human body, two hands, two
forearms, tow upper arms, tow feet, two
shanks, two thighs, one torso, one neck,
and one head are considered as elemental
parts. Î Anthropometric data
CG of human body
• Human body is not rigid object Î the location of
CG is ___________ depending on the position of
its arms
• It can be located outside of body depending on
posture
• Location of CG ~ ___________ of your height
from the ground
– Female ~ 55% due to larger pelvic girdles and narrower
shoulders
– Male ~ 57% due to wider shoulder
CG and Performance
• Jump-and-reach test techniques