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centripetal acceleration and centripetal force

centripetaceleration and centripetal force

By ka cheung chan

Linear velocity

 

 

    The vector of any mass is equal to the tangant the radius. Thus although the magnitute of the velocity does not change, its direction change toward the centre.  Velocity changes over time.  There is an acceleration.

Centripetacceleration

 

  Va is the instant velocity of position a whereas Vb is that of position b. After a short interval of time, a move to b and the vector changed delta v. Owing to the angle change is so small that delta v can be seem as perpendicular to both Va and Vb.  Hence, that is the direction to the centre.

Centripetal force

   According to Newton's second law 

Newton's laws of motion

Newton's laws of motion

By kacheung chan

The First law

    Other than exerting external force, mass will remain its state of uniform Linear velocity or static. It is known as inertia.

The Second law

 

Where p=Momentum, m=Mass, V=velocity
Let the initial and final velocityof the mass is U and V. Then,
 

   

                   

The Third Law

    When two mass collide together, both of them suffer from equal but inverse force. This is called action and reaction force.
 

          
 

 The law of conservation of momentum

    It is stated that within a enclosed isolated system, all momemtum will remain the same after a collision. As mentioned by Newton third law, two collision forces F1 and F2 are equal but reverse.

Initial monentum=final momemtum

Circular Motion

Circular Motion

 By ka cheung chan

 Suppose a mass move from A to B in  circumstance, the path is the length of the arc which is called s. The corresponding angle at the centre is the displacement of angle.

It can be expressed by degree or radian. The relationship between s, radius, and the angl displacement is shown below.

Angular velocity

    The velocity of mass in the displacement s over the period of time is angular velocity

Period

   The duration when the mass move around the circle for one cycle is called period.  

Frequency

    It is no of cycle the mass moved over a unit of time.

So, angular velocity can be expressed as 

Force-statics

By kacheung chan

Type of force

Weight (W)-the weight of mass is universiall gravitation exerted by earth to the mass. The vector of this force points to the earth core.

Reaction force (R)-as a mass is placed on a surface (even leveling or inclined) , it is suffered from a force which is vertical to the surface. If R is equal to the W inversely, they compensate one another and remain static. Otherwise they keep moving.

Tension force (T)-when a mass is suffered from a pulling force that make all its parts tightened. It is the force pointed to the pulling force and opposited to the mass.

Elastic force (Fe)-as a mass is deformed owing to a stress exerted upon it, it will then recover naturally, it is known as elastic force.K is a constant, e is elasticity.

Fractional force (f)-it occurs between two different touching surface and opposite corresponding moving force of two mass.Where fL is the maximum fraction that the mass keep static. After that it moves and the fractional force (fk) keep contant.

fL is portional to the surface texture and the reactional force, whereas Us is the coefficient.of fraction before moving and fk is coefficient after moving.