2 Circular Motion - PDF

Uniform Circular Motion: Motion of an object in a circular track that covers equal distance in equal time interval.
➢It is two dimensional motion.
➢Continuously changing the direction of motion.
➢Though it is a uniform motion, it is under the action of force acting towards the
Centre of the circular path is called centripetal force.
➢ Centripetal force is used to change the direction of motion but not to change
the speed of the object.
➢The change in direction causes the change in velocity ( but magnitude remains
constant).
The change in velocity causes acceleration.
Though circular motion is an accelerated motion, why does the speed or kinetic energy of the object not change?
?...
Examples:
1. Motion of electrons around the nucleus.
2. Motion of planets around the sun.
3. Spinning of DVD in computer.
4. Spinning of drum in washing machine. Etc.

Wall of Death
TERMS REALTED TO CIRCULAR MOTION
1. Angular displacement (ϴ)- Angle subtended at the center of a circular path by the position of the object in
circular motion is called angular displacement.
SI unit of angular displacement is radian(rad)
Define radian
One radian( 1 rad)- Angle subtended at the center of circle by an arc length equal to its radius.
𝐴𝑟𝑐 𝑙𝑒𝑛𝑔𝑡ℎ
ϴ= , 𝑖𝑓 𝑎𝑟𝑐 length = radius, ϴ = 1 radian= 57o
𝑟𝑎𝑑𝑖𝑢𝑠
2. Angular velocity (ω)-
Rate of change of angular displacement is called angular velocity.
𝑑ϴ
ω = SI unit is radian per second.
𝑑𝑡
3. Period (T)- Time taken to make one complete revolution in a circle is called period.
5 second is taken for 1 revolution means T = 5 s
4. Frequency (f)- no of completer revolution per second is called frequency. It is the reciprocal of period.
SI unit is cycle per second or Hertz (Hz).
1
f=
𝑇
Relation among ω, T and f,
For one complete revolution in a circular track,
2π 1 2π
ω = = 2π . = = 2π .f [ω does not depend on size of circular path ]
𝑇 𝑇 𝑇
Relation between angular speed(ω) and linear speed (v)
5. Centripetal acceleration(ac) and centripetal Force (FC):
AS an object is moving in a circular path, it keeps changing direction of

motion. The change in direction causes the change in velocity of the object
and finally causes acceleration. So, uniform circular motion is an accelerated
motion.
The acceleration is always directed towards the centre of circular path along
the radius so it is known as centripetal acceleration.
The ultimate cause behind this acceleration is a force directed towards the
centre of the circle so it is known as centripetal force(Fc).
The direction of force and acceleration are always same.

i.e. directed towards the centre of circle.
𝑣2
Formula for centripetal acceleration( ac) = = r ω2
𝑟
Derivation (Optional)
𝑚𝑣 2
Centripetal Force (Fc) = mass(m) x acceleration (ac ) = = m r ω2
𝑟
A constant force acting on the object which keeps object moving in a circular track.
It is always directed towards the centre of path and provided by some external sources.
The sources (causes) of centripetal force in different cases.
1. Electron revolves around the nucleus – The necessary centripetal force is provided by electro static force of
attraction.
2. Planet revolves around the Sun- The necessary centripetal

force is provided by gravitational force of attraction.
1. Orbital speed of the satellite in its orbit.
𝐺𝑀
V=
(𝑅+ℎ)
Solution:
Ans: Tension=12.3N
Period = 1.8 s
What should be the minimum speed of the object at the highest position to maintain the vertical circular motion?
Examples of vertical circular motion:
1. If a water bucket full of water is whirled in a vertical motion beyond certain velocity, water does not
fall down even the bucket is upside down at the highest position.
2. People with out fastening belt do not fall down from the roller
coaster even in upside down position.
Application of circular motion:
1. Cream can be separated from milk
2. Honey can be separated from wax.
3. Water is removed from wet cloths while spinning washing machine.
4. Centrifuge machine to separate small and heavy particles from the mixture.
This diagram shows a rubber bung, of mass 200 g, on the end of a length of string being
swung in a horizontal circle of radius 40 cm. The string makes an angle of 56° with the vertical.
Calculate:
(i) the tension in the string
(ii) the angular speed of the bung
(iii) the time it takes to make one complete revolution.
Practice questions.pdf
Q-2
Q-3
Q-4
This diagram shows part of the track of a roller-coaster ride in which a truck loops the loop. When the truck is at
the position shown, there is no reaction force between the wheels of the truck and the track. The diameter of
the loop in the track is 8.0 m.
(a) Explain what provides the centripetal force to keep the

truck moving in a circle. Given that the acceleration due to
gravity g is 9.8 m s−2,
(b) calculate the speed of the truck.

Q-5
a. Show that in one revolution there are 2π radians.
b. This diagram shows a centrifuge used to separate solid particles suspended in a

liquid of lower density. The container is spun at a rate of 540 revolutions per
minute.
(i) Calculate the angular velocity of the container.

(ii) Calculate the centripetal force on a particle of mass 20 mg
at the end of the test tube.
(iii) An alternative method of separating the particles from the

liquid is to allow them to settle to the bottom of a
stationary container under gravity. By comparing the forces
involved, explain why the centrifuge is a more effective
method of separating the mixture.

2 Circular Motion - PDF

Uploaded by

Copyright:

Available Formats

2 Circular Motion - PDF

Uploaded by

Document Information

Original Title

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

2 Circular Motion - PDF

Uploaded by

Copyright:

Available Formats

Uniform Circular Motion: Motion of an object in a circular track that covers equal distance in equal time interval.

➢It is two dimensional motion.

➢Continuously changing the direction of motion.

2. Motion of planets around the sun.

3. Spinning of DVD in computer.

4. Spinning of drum in washing machine. Etc.

SI unit of angular displacement is radian(rad)

2. Angular velocity (ω)-

Rate of change of angular displacement is called angular velocity.

5 second is taken for 1 revolution means T = 5 s

For one complete revolution in a circular track,

AS an object is moving in a circular path, it keeps changing direction of

The direction of force and acceleration are always same.

The sources (causes) of centripetal force in different cases.

2. Planet revolves around the Sun- The necessary centripetal

1. Cream can be separated from milk

2. Honey can be separated from wax.

3. Water is removed from wet cloths while spinning washing machine.

(a) Explain what provides the centripetal force to keep the

(b) calculate the speed of the truck.

b. This diagram shows a centrifuge used to separate solid particles suspended in a

(i) Calculate the angular velocity of the container.

(iii) An alternative method of separating the particles from the

You might also like