Linear Motion
For constant velocity. Distance moved at constant velocity
For constant Acceleration from velocity v_o start.
v = v_o + a . t
s = v_o . t + 1/2 . a . t2
v2 = v_o2 + 2 . a . s
Simple Harmonic Motion
Simple Harmonic Motion is characterised by the relationship that the rate of accelaration of a body towards a central position is directly related to the distance of the body from the central position. The result is a cyclic motion with a frequency = 2 . p / n.
f ''(x) = - n2 . x
The solution for the displacement from and the velocity towards the central position is below;
x = a . cos ( n. t + e )
x ' = - n . a . sin ( n. t + e )
Newtons laws of Motion
Newtons First Law;
The rate of change of momentum of a body is proportional to the force
acting on a body an is in the direction of that force.
Newtons Second law;
Every body continues in a state of rest or of uniform rectilinear motion
unless acted upon by a force.
Newtons Third law
To each action (or force) there is an equal and opposite reaction.
Momentum
Momentum = m . v
Force
F = m . a
Definition of Mass Moment of Inertia
The mass moment of inertia of a body about an axis has been defined as the sum of the products of mass-elements and the square of their distance from the axis
For a disc I = m. r2/2
Rotary Motion
For a mass rotating about a centre. The force tending to accelarate the mass
towards the centre and restraining the mass to move around the centre is the centripetral force.
The reaction to this force tending the accelarate the mass away is the centrifugal force.
(If the string breaks the mass would fly away under the effect of the centrifugal force.
Accelaration Torque
Angular accelaration a = (w2-w1) / t
Accelaration Torque T = I . a