C16 Circualr Motion Flashcards
What’s angular speed similar to
Angular frequency
Linear velocity relationship with a circular path
Linear velocity is always at tangent to circular path.
For object moving in a circle at constant speed, calc speed using:
Speed= Distance travelled/ Time taken
One complete rotation: v=2pi r / T
And since angular velocity= 2pi / T
v= r x angular velocity.
Objects with same angular velocity, the linear velocity at any instant is
directly proportional to radius.
What direction does the acceleration of any object travelling in a circular path at constant speed.
Always acts to centre of circle.
Centripetal Acceleration depends on:
Depends on the speed (v) of object and radius:
Acceleration= velocity^2 / radius
Combine with v = circular velocity x r
Therefore a= circular velocity^2 x r
Newton’s second law
F (resultant force) is directly proportional to the change in momentum / time.
For angular velocity the faster the object moves, the…
Greater the angle moved through, in a given time
(Accelerating at a constant velocity) When moving in a circular path, direction is always changing therefore we can say…
Velocity is changing (even if speed is constant), change in velocity means object must be accelerating, and greater rate change of velocity the greater the acceleration.
Centripetal force
Any force, keeps body moving with uniform speed along circular path
What does any accelerating body require
A net force action on it
What’s the relationship between centripetal force and an objects velocity
Always perpendicular to each other
What’s does the fact the CF always acts perpendicular to the velocity of object mean?
This force has no component in the direction of motion and so no work being done on object, therefore resultant speed remains constant.
Centripetal Force equation
Fc=mv^2 / r
(from F=ma and a= circular velocity^2 x r)
When an object is spinning round on a vertical axis, what force is constant, and what force isn’t constant?
Centripetal force is constant
Tension not constant
where does the equation for centripetal force come from?
Fc=mv^2 / r (from F=ma and a= circular velocity^2 x r) where Fc is the centripetal force
Object spinning round on vertical axis, what forces are constant and not constant?
centripetal force constant, tension not constant.
Tension acts on both ends of string, interested with one at end of ball. Centripetal acceleration acts towards centre, therefore centripetal force also acts in that direction.
Explain what happens at each 3 stages of an object being swung with circular motion, in the vertical plan
A- at top, both weights of the mass and the tension in the string are pulling the mass downwards towards the centre of circle.
Therefore: Fc = mg + T (tension)
And so: (m x r x circular velocity^2) + T
Giving: T = (m x r x circular velocity^2) - mg
B- at bottom, weight always acts downwards, tension acts towards the centre
F (resultant) = T - mg
C- Horizontal string, weight is acting perpendicular to direction of the centre of the circle, no effect. F(resultant) = T
F= m x r x circular velocity^2
Banked Surfaces:
For high speed travel, race tracks have banked corners, why?
this way the moving object weight is helping friction keep the object moving in a circle.
-Without any banking the centripetal force provided by friction alone.
-Banked corners allow the same radius of curvature to be followed at greater speeds, assuming Fr is negligible, the centripetal force provided by horizontal component of the normal reaction force.
And the vertical component balances the weight.
N x sin(theta) = mv^2 / r
N x cos(theta) = mg
what is an equation for velocity^2, and how do you derive the equation?
v^2 = gr x tan(theta)
link the Nsin(theta) and Ncos(theta) equations, using trig identity
Two conclusions you can deduce from Banked Surfaces, in circular velocity:
1) Steeper bank, faster can go round any given radius of curvature.
2) Assumes that there is no other force acting other than horizontal component of weight of car. A car travelling at just the right speed could negotiate this curve even if there was no friction
Moving charged particles deflected in magnetic field in accordance with what?
Fleming’s left hand rule.
For a charged particle how is circular motion achieved?
The force acts perpendicular to the velocity causing the circular path to change (circular motion is achieved).
For what cases does the path of a charged particle in a magnetic field, become more curved?
The path becomes more curved (r reduced) if flux density increases or if velocity decreases or if particles with a larger specific charge are used.
Create an equation for the radius of curvature, from the equation of force on a charged particle, and centripetal force.
F=BQv
F=mv^2 / r
Therefore r = mv / BQ
Mass Spectrometer:
machines used analyse types atoms, (and isotopes) present in sample
-As always with circular motion problems we are looking to equate to Fc.
What is the equation for the force applied from an electric field on a charged particle?
F = QV / d
What is the equation for the force applied from a magnetic field on a charged particle?
F = BQv
what component is used to obtain a constant velocity?
Component known as a velocity component
In a Mass Spectrometer, the +ve ions are acted upon by both an electric field and magnetic field.
Only when they’re equal and opposite do ions pass through the slit, which results to what equation?
V / d = Bv
(V. voltage)
(v, velocity)
(d, distance)
