NEET

1. .crashup.in
Physics, Class 11, Chapter 7
System of Particles
and Rotational Motion
For IIT JEE, NEET, Boards & Olympiad | Made with love by Vikrant Kirar
Click here to watch the YouTube video
Rigid Body
A body with perfectly definite and unchanging shape.
The distance between two points of a rigid body does
not change.
रिजिड बॉडी के ककन्ही भी दो पॉइंट्स के बीच की दूिी बदलती नहीं है।
इसके जलए वह इंटिनल फोसेि का इस्तेमाल किती है।
Types of Motion
Translational Motion
Every point on the body has same velocity. No
rotation.
बॉडी के पॉइंट्स की वेलोजसटी बिाबि होती है।

2. .crashup.in
Circular Motion
Circular path, but no rotation. Mostly meant for point
objects.
िोटेशन नहीं होता है। चाय कप से गििेिी नहीं।
Rotational Motion
Circular Motion with rotation of body.
बॉडी िोटेट भी कि िही है। चाय गिि िाएिी।
Combination
Rotation and translation together.
Examples
Pure rotation: Fan
Pure translation: Wagon of a train
Pure rolling: Wheel of a train
Pure circular motion: difficult to find in nature

3. .crashup.in
Overview
Translational Angular
Position Angular Position
Displacement Angular Displacement
Velocity Angular Velocity
Acceleration Angular acceleration
Mass (inertia) Moment of Inertia
Momentum Angular Momentum
Force Torque
Kinetic Energy Rotational Kinetic Energy

4. .crashup.in
Right-Hand Rule
All angular quantities have
magnitude and direction. But
they are not vector.
A + B ≠ B + A.
is not vector.
& are pseudo vectors.
We will only study rotation about a fixed axis. For fixed
axis of rotation, we can treat them as vectors.

5. .crashup.in
Kinematics
Uniform Angular Acceleration
General Equations

6. .crashup.in
Linear and Angular Motion
We’re interested in distance, not displacement.
Distance = arc length =
Angular Velocity
Angular Acceleration (Tangential)
Centripetal Acceleration (Radial) भूलना मत

7. .crashup.in
Frequency
How many times per second (or per day/minute)
SI Unit: Hz (hertz).
1 Hz = 1 per second.
Time Period
Frequency = f
Time Period = T
T = 1/f
One Revolution
2π radian = 1 revolution
𝜔 = 2𝜋𝑓
𝑇 =
2 𝜋
𝜔
=
1
𝑓

8. .crashup.in
Angular Velocity
Relative to the viewer. Always because of the
perpendicular component of the velocity.

9. .crashup.in
Torque
Analogue of force in angular terms. Moment of Force.
जितना दूि से force लिता है, उतना ज्यादा torque होता है।

10. .crashup.in
Torque Vector
Graphical Method
Analytical Method
Cross Product or vector product.
वीकडयो से समझने के जलए यहाँ क्लिक किें।

11. .crashup.in
Moment of Inertia
Resistance to rotate. Inertia to rotate.
Depends upon mass and its distribution.
मास एक्लिस से जितना दूि होिा, उसे घूमना उतना ही मुश्किल होिा।
Discrete Mass Distribution
Continuous Mass Distribution

12. .crashup.in
Rigid Body Dynamics
Every particle of the
body moves in a circle
which lies in a plane
perpendicular to the
axis and has its center
on the axis.

13. .crashup.in
Moment of Inertia
Uniform Rod
Triangle
Ring / Hollow Cylinder
Disc / Solid Cylinder
Hollow Sphere
Solid Sphere

14. .crashup.in
Perpendicular Axes Theorem
For 2D (planer) objects

15. .crashup.in
Parallel Axes Theorem
For any 3D/2D object.
When Axis is shifted parallelly.

16. .crashup.in
Radius of Gyration (k)
Defined to keep calculations simple.

17. .crashup.in
Center of Mass
CoM moves as if all the mass of the system was
concentrated at CoM and all external forces were
applied at that point.
F=Ma
Other parts may feel some different forces due to
internal forces.
Center of Gravity
Point where the total gravitational torque on the body
is zero. For Uniform gravitational field, it’s same as
CoM.
CoG = CoM CoG = CoM

18. .crashup.in
Equilibrium of a Rigid Body
The linear and angular momentum must be constant.
For mechanical equilibrium, net force and net torque
should be zero.
Examples of a rod not in equilibrium.

19. .crashup.in
Topple
If friction is sufficient, the body may rotate before
translation starts.
सिकने से पहले लुढ़क िाती है।
The normal reaction shifts to avoid topple.

20. .crashup.in
Levers
Mechanical Advantage = Load / Effort
3 points: Load, Fulcrum &Effort

21. .crashup.in
Couple
A pair of equal and opposite forces with different lines
of action is known as a couple.
Net force is zero. CoM does not move.
It does not matter where you apply the force, Torque
is always the same.

22. .crashup.in
Rotational Dynamics

23. .crashup.in
Equivalent Mass
Imaginary concept to solve questions quickly.

24. .crashup.in
Kinetic Energy
Total KE = Rotational KE + Translational KE
For Hinged motion, using the parallel axes theorem,
the above formula becomes

25. .crashup.in
Rolling Motion
No Slip Condition
Cycloid Trajectory

26. .crashup.in
Instantaneous Axis of
Rotation
Every point is doing circular motion about some point.
जसफफ उस क्षण के जलए उसे हहन्ज माना िा सकता है।

27. .crashup.in

28. .crashup.in
Translation to Rolling
िब तक pure rolling शुरू नहीं होती, तब तक acceleration औि
angular acceleration constant िहेंिे। क्योंकक अभी pure rolling
नहीं हो िही है, Instantaneous Axis of Rotation का इस्तेमाल नहीं
कि सकते।
मान लो pure rolling शुरू होने में समय लिा 't'

29. .crashup.in
Rolling to Translation
िब तक pure rolling शुरू नहीं होती, तब तक acceleration औि
angular acceleration constant िहेंिे। क्योंकक अभी pure rolling
नहीं हो िही है, Instantaneous Axis of Rotation का इस्तेमाल नहीं
कि सकते।
मान लो pure rolling शुरू होने में समय लिा 't'

30. .crashup.in
Pure Rolling on an Incline
Pure rolling हो िही है, इसीजलए Instantaneous Axis of
Rotation इस्तेमाल ककया िा सकता है।

31. .crashup.in
Which is Faster?
Work-Energy Theorem का इस्तेमाल किें

32. .crashup.in
YoYo
Maximising rotational KE for fun. No-slip है, पि छोटे वाले
radius पि। v=rw भी छोटे वाले िेकडयस पि ही लिेिा।

33. .crashup.in
Angular Momentum
Moment of Momentum
L = R x P
Parallel axes theorem के कािण ये दोनों ही बिाबि आते हैं।

34. .crashup.in
Flywheel
To stabilize angular velocity. ताकि झटिे न लगें।

35. .crashup.in
Example
Linear and Angular momentum (about any point) will
be conserved.

36. .crashup.in
Example
Hinge can apply some forces. Only Angular
momentum about hinge will be conserved.

37. .crashup.in
Power

38. .crashup.in
Gyroscopic Precession

39. .crashup.in
Vikrant Kirar
IIT Kharagpur
बकिया नोट्स और वीकियोस िे कलए यहााँ क्लिि िरें।