Linear and Angular Concepts Applied to Biomechanics
Linear
Angular
1. Time (t)
1. Time (t)
2. Position
2. Orientation
3. Linear displacement (d)
3. Angular displacement ()
4. Linear velocity (V)= d/t
4. Angular velocity ()=/t
5. Linear acceleration (A)= V/t
5. Angular acceleration ()=/t
6. Force = mass x acceleration
6. Torque ()= force x perpendicular
distance
An imbalancing force causes linear
An imbalancing torque causes
acceleration.
rotational acceleration.
7. Newton’s 1st Law - the law of
7. Newton’s 1st Law - the law of
inertia
inertia
A body at rest remains at rest and a
A body at rest remains at rest and a
body in motion remains in motion in a
body that is rotating remains rotating
straight line unless acted upon by an
unless acted upon by an outside torque.
outside force.
Inertia is the property of a body that
resists changes in position or linear
motion.
Moment of inertia (I) is the property
of a body that resists changes in position
or angular motion.
Mass (M) is a measure of inertia.
I=Mr2
Note that I is a product of the mass of
the rotating object and square of the
distance that the mass is located from the
point of rotation.
8. Newton’s 2nd Law - law of angular
acceleration (also known as the Law
of Angular Momentum)
8. Newton’s 2nd Law - the law of
linear acceleration (also known as
the Law of Momentum)
The linear acceleration of an object is
The angular acceleration of an object
directly proportional to the force and
directly proportional to the torque and
inversely proportional to mass.
inversely proportional to the moment of
inertia.
F = M x A, where F is force, M is mass
and A is acceleration.
Note that F = M x V/t and Ft =MxV
Ft is a quantity called impulse and MV
is momentum.
In other words, the application of force
to an object for a period of time causes
the object to change its linear
momentum.
 = I x , where I is the moment of
inertia and  is the angular acceleration.
Note that T = I x /t and Tt = I
I is a quantity called angular
momentum.
In other words, the application of a
torque to an object for a period of time
causes the object to change its angular
momentum.
9. Conservation of linear momentum
In any system the linear momentum
does not change unless an outside force
is applied to the system.
9. Conservation of angular momentum
In any system the angular momentum
does not change unless an outside torque
is applied to the system.
10. Conservation of energy
The energy of a system is conserved.
Application of the conservation of
angular momentum to the kinetic link
principle
10. Conservation of energy
The energy of a system is conserved.
Potential energy (PE) = Mgh, it is
energy do to position.
Kinetic energy (KE) = 1/2MV2,, it is
energy do to linear velocity (motion).
11. Newton’s 3rd Law - the law of
action and reaction
For every action (force) there is an
equal and opposite reaction (force).
Angular kinetic energy = 1/2xI2, it is
energy do to angular velocity (motion).
11. Newton’s 3rd Law
For every torque there is an equal and
opposite torque.
Dr. Eugene W. Brown
Department of Kinesiology
Michigan State University
Linang.doc