C16 Circualr Motion

Question 1

What’s angular speed similar to

Answer 1

Angular frequency

Question 2

Linear velocity relationship with a circular path

Answer 2

Linear velocity is always at tangent to circular path.

Question 3

For object moving in a circle at constant speed, calc speed using:

Answer 3

Speed= Distance travelled/ Time taken
One complete rotation: v=2pi r / T
And since angular velocity= 2pi / T
v= r x angular velocity.

Question 4

Objects with same angular velocity, the linear velocity at any instant is

Answer 4

directly proportional to radius.

Question 5

What direction does the acceleration of any object travelling in a circular path at constant speed.

Answer 5

Always acts to centre of circle.

Question 6

Centripetal Acceleration depends on:

Answer 6

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

Question 7

Newton’s second law

Answer 7

F (resultant force) is directly proportional to the change in momentum / time.

Question 8

For angular velocity the faster the object moves, the…

Answer 8

Greater the angle moved through, in a given time

Question 9

(Accelerating at a constant velocity) When moving in a circular path, direction is always changing therefore we can say…

Answer 9

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.

Question 10

Centripetal force

Answer 10

Any force, keeps body moving with uniform speed along circular path

Question 11

What does any accelerating body require

Answer 11

A net force action on it

Question 12

What’s the relationship between centripetal force and an objects velocity

Answer 12

Always perpendicular to each other

Question 13

What’s does the fact the CF always acts perpendicular to the velocity of object mean?

Answer 13

This force has no component in the direction of motion and so no work being done on object, therefore resultant speed remains constant.

Question 14

Centripetal Force equation

Answer 14

Fc=mv^2 / r

(from F=ma and a= circular velocity^2 x r)

Question 15

When an object is spinning round on a vertical axis, what force is constant, and what force isn’t constant?

Answer 15

Centripetal force is constant
Tension not constant

Question 16

where does the equation for centripetal force come from?

Answer 16

Fc=mv^2 / r (from F=ma and a= circular velocity^2 x r) where Fc is the centripetal force

Question 17

Object spinning round on vertical axis, what forces are constant and not constant?

Answer 17

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.

Question 18

Explain what happens at each 3 stages of an object being swung with circular motion, in the vertical plan

Answer 18

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

Question 19

Banked Surfaces:

For high speed travel, race tracks have banked corners, why?

Answer 19

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

Question 20

what is an equation for velocity^2, and how do you derive the equation?

Answer 20

v^2 = gr x tan(theta)

link the Nsin(theta) and Ncos(theta) equations, using trig identity

Question 21

Two conclusions you can deduce from Banked Surfaces, in circular velocity:

Answer 21

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

Question 22

Moving charged particles deflected in magnetic field in accordance with what?

Answer 22

Fleming’s left hand rule.

Question 23

For a charged particle how is circular motion achieved?

Answer 23

The force acts perpendicular to the velocity causing the circular path to change (circular motion is achieved).

Question 24

For what cases does the path of a charged particle in a magnetic field, become more curved?

Answer 24

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.

Question 25

Create an equation for the radius of curvature, from the equation of force on a charged particle, and centripetal force.

Answer 25

F=BQv
F=mv^2 / r

Therefore r = mv / BQ

Question 26

Mass Spectrometer:

Answer 26

machines used analyse types atoms, (and isotopes) present in sample

-As always with circular motion problems we are looking to equate to Fc.

Question 27

What is the equation for the force applied from an electric field on a charged particle?

Answer 27

F = QV / d

Question 28

What is the equation for the force applied from a magnetic field on a charged particle?

Answer 28

F = BQv

Question 29

what component is used to obtain a constant velocity?

Answer 29

Component known as a velocity component

Question 30

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?

Answer 30

V / d = Bv

(V. voltage)
(v, velocity)
(d, distance)