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
An imbalancing force causes linear
acceleration. / 6. Torque ()= force x perpendicular
distance
An imbalancing torque causes
rotational acceleration.
7. Newton’s 1st Law - the law of
inertia
A body at rest remains at rest and a body in motion remains in motion in a straight line unless acted upon by an outside force.
Inertia is the property of a body that resists changes in position or linear motion.
Mass (M) is a measure of inertia. / 7. Newton’s 1st Law - the law of
inertia
A body at rest remains at rest and a body that is rotating remains rotating unless acted upon by an outside torque.
Moment of inertia (I) is the property
of a body that resists changes in position or angular motion.
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 - the law of
linear acceleration (also known as
the Law of Momentum)
The linear acceleration of an object is directly proportional to the force and inversely proportional to mass.
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. / 8. Newton’s 2nd Law - law of angular
acceleration (also known as the Law
of Angular Momentum)
The angular acceleration of an object
directly proportional to the torque and
inversely proportional to the moment of inertia.
 = 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.
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). / 10. Conservation of energy
The energy of a system is conserved.
Angular kinetic energy = 1/2xI2, it is energy do to angular 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). / 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