Download Computing Torque

KINE 3301
Biomechanics of Human Movement
Computing Torque
Chapter 11
Torque: Forces that cause rotation
The force F shown below is
applied directly thru the center
of mass of the object. The
object will translate in the
direction of the force.
The force F shown below is not
applied directly thru the center
of mass of the object. The
object will translate in the
direction of the force and rotate.
The object does not rotate.
The object rotates & translates.
Definition of Torque
• Torque is defined as a force that causes or will tend to
cause rotation.
• Torque is also referred to as moment of force or a
moment.
• Torque is computed by multiplying the magnitude of the
force by the lever arm as follows:
𝜏 = 𝐹 ×𝑙
Where 𝜏 is the torque in N∙m, 𝐹 is the magnitude of
the force in N, and 𝑙 is the lever arm in m. Torque is a
vector with its direction defined by the right hand
rule, CCW rotation is positive, CW is negative.
To compute torque determine: the axis of rotation (point of
torque calculation), line of action of the force, magnitude of
force, lever arm (moment arm or perpendicular distance), and
the direction of rotation the force causes about the axis of
rotation.
Compute the Torque about Points A & B
The 100 N force causes a positive (CCW) +20
N∙m torque about point A.
The 100 N force causes a negative (CW)
−50 N∙m torque about point B.
A force that passes thru the point of torque calculation
(axis of rotation) causes no torque about that point.
Compute the Torque about C
It is not uncommon for
two or more forces to act
about the point of torque
calculation.
Torque When Two or More Forces Act
Any force that does not
pass thru the elbow joint
center will cause torque in
the figure below.
Compute the Torque about A & B
The |100 N| force causes
negative rotation about
point A.
The |100 N| force causes
positive rotation about
point B.
Compute the Sum of Torques about A
Στ =?
Compute the
Sum of the
Torques about
the Center of
the Fan
Angular Version of Newton’s Laws of Motion
• I. Law of Inertia: A body at rest stays at rest, a
rotating body stays in rotation unless acted upon by
a net torque.
• II. Law of Acceleration: The angular acceleration (𝛼) a
body experiences is directly proportional to the
torque (τ), inversely proportional to the moment of
inertia (Ι), and in the direction of the net torque.
Στ = Ι𝛼
• III. Law of Reaction: For every torque there is an
equal and opposite torque.
Law of Inertia
• Inertia is the natural tendency of an object to
remain at rest, or rotating at a constant
angular velocity (𝜔).
• Moment of Inertia is defined as an object’s
resistance to angular change.
• The units for moment of inertia (I) are kg∙m2
• It is a function of mass and length and how
the mass is distributed about an axis of
rotation.
Calculation of Moment of Inertia
Examples of
Moment of
Inertia
The actual value
of ICM will
depend upon
the height and
mass of the
individual.
Moving the body
segments closer
to the axis of
rotation
decreases the
moment of
inertia.
Which Object is More Difficult to Rotate?
Law of Acceleration
• The angular acceleration (𝛼) a body experiences is
directly proportional to the torque (τ), inversely
proportional to the moment of inertia (Ι), and occurs in
the direction of the net torque.
Στ = Ι𝛼
Law of Acceleration
• The angular acceleration (𝛼) a body experiences is
directly proportional to the torque (τ), inversely
proportional to the moment of inertia (Ι), and occurs in
the direction of the net torque.
Στ = Ι𝛼
Law of Acceleration
• The angular acceleration (𝛼) a body experiences is
directly proportional to the torque (τ), inversely
proportional to the moment of inertia (Ι), and occurs in
the direction of the net torque.
Στ = Ι𝛼
Law of Reaction
• For every torque there is an equal and opposite torque.
Opposite & Equal Joint Torques
The torques are
equal and
opposite across
each joint.
The red torque
plantar flexes the
foot about the ankle,
the blue torque
plantar flexes the
lower leg about the
ankle.
Complete the FBD, Compute Rx, Ry, α for the
diver shown below.
Bicep Force to Hold 30 lbs (133N)
Rotational Work for a Non-Constant Torque
Ave = 53 N∙m
For a non-constant torque use the average torque (𝜏) of 53 Nm to compute rotational
work. The joint rotated from an initial angle (𝜃𝑖 ) of 1.54 r to a final angle (𝜃𝑓 ) of 0.1 r,
compute the rotational work.
𝑊𝑅 = 𝜏 𝜃𝑓 − 𝜃𝑖
𝑊𝑅 = 53𝑁 ∙ 𝑚 0.1𝑟 − 1.54𝑟
𝑊𝑅 = −76.32 𝑁 ∙ 𝑚
Compute the rotational work for the concentric
(knee extension) and eccentric (knee flexion)
phases of the exercise shown below.