2. Idea about circular motion
Circular Motion :
Motion of an object in a circular path is called circular motion.
Circular motion is also known as:
Angular motion
Rotatory motion
3. Angular displacement
The distance between two points in a circular path is measured by “ ”and is called
angular displacement.
It is usually denoted by “ ”
𝝦 = S / r
It is a vector quantity.
Units
“Radian(SI unit), Degree, Revolution”.
Its direction is determined by RHR(right hand rule).
Direction is +ve in counter clock wise direction
𝝦
𝝦
4. Relation of Radian, Degree
and revolution
By completing one round:
One round = one revolution
One revolution = 2𝝅 rad
2𝝅 rad = 360 degree
1 rad = 360 / 2 𝝅 = 57.3 degree
5. Angular velocity
Time rate of change of angular displacement is called angular velocity.
It is denoted by “𝞈”
𝞈 = Δ𝝦 / Δt
Unit is “rad per sec (SI Unit)” , “revolution per minute”
Direction is determined by RHR
It is a vector quantity and direction will be along the axis of rotation
Average angular velocity?
Instantaneous angular velocity?
6. Angular acceleration
Definition:
Time rate of change of angular velocity is called angular acceleration.
It is denoted by “α”
α = Δ𝞈 / Δt
Unit is [“rad/𝒔𝒆𝒄 𝟐
”] or [revolution/𝑚𝑖𝑛𝑢𝑡𝑒 𝟐
]
It is a vector quantity direction will be along the axis of rotation
Direction is determined by RHR
Average angular acceleration?
Instantaneous angular acceleration?
7. Relation b/w angular and linear velocity
When an object moves in a circular path, its point “P” linear distance in time
interval “Δt” will be ΔS, while angular displacement will be Δ𝝦.
ΔS = rΔ𝝦
Dividing equation with Δt, we get
V = r 𝞈
9. Centripetal force
The force which keeps the body to move in a circular path is called centripetal
force.
Fc = 𝐦𝒗 𝟐
/ r
In angular motion
Fc = mr𝒘 𝟐
Centripetal acceleration:
The acc. Of moving object in a circular path and whose direction is towards center is
called centripetal acceleration.
Fc = mac
10. Moment of inertia
The product of mass and square of radius is called moment of inertia.
I = m𝑟2
Unit is kg𝑚2
It is scalar quantity
Notes:
It is rotational analogous of mass
It depends upon mass and square of radius
11. Angular momentum
The cross product of position vector ‘’r’’ and linear momentum “p” is called
angular momentum.
L = r x p
Its magnitude is “L = rpsin$”
Its SI Unit is kg𝒎 𝟐
𝒔−𝟏
or Js
It is a vector quantity
Notes: if $ = 90
L = rp = mvr As v = r𝞈
L = m𝒓 𝟐
𝞈
12. Spin angular momentum
vs. orbital angular momentum
Spin angular momentum Orbital angular momentum
When an object about its own axis,
angular momentum is called spin
angular momentum
When an object moves about an
external axis/orbit, angular momentum
is called orbital angular momentum
It is represented by Ls It is represented by Lo
Radius is small, so body is considered a
point
Radius is larger than Ls
13. Law of conservation of angular momentum
If no external torque is applied on the system, total angular momentum of the
system remain conserve.
𝐼1 𝞈 1 = 𝐼2 𝞈 2
It is a vector quantity.
It direction is along the axis of rotation.
e.g.
Motion of earth around the sun.
14. Rotational K.E
Definition:
Energy gained by an object while moving in a circular path is called rotational K.E.
K.Erot = ½ I𝞈 𝟐
15. Rotational K.E of disc and hoop
For disc:
I = ½ m 𝒓 𝟐
So, K.E = ½ * (½ m𝒓 𝟐
) ∗𝞈 𝟐
K.E = ¼ m𝒓 𝟐
𝞈 𝟐
As 𝒓 𝟐
𝞈 𝟐
= 𝑽 𝟐
K.E = ¼ m𝒗 𝟐
For hoop:
I = m 𝒓 𝟐
K.E = ½ * ( m𝒓 𝟐
) ∗𝞈 𝟐
K.E = ½ m𝒓 𝟐
𝞈 𝟐
As 𝒓 𝟐
𝞈 𝟐
= 𝑽 𝟐
K.E = ½ m𝒗 𝟐
16. Velocities of disc and hoop
If both start moving down the inclined, their motion consist of both rotational and
translational motions. If there is no energy loss, then
For disc
For hoop
17. G.K.K / H.K.K
Artificial satellites
Real and apparent weight
Weightlessness in satellites and gravity free system
Orbital velocity
Artificial gravity
Geo stationary orbits
Newton’s and Einstein views of gravitation
18. Fluid dynamics
What is fluid?
Anything which can flow is called fluid.
E.g. all liquids and gases
Fluid dynamics?
The study of fluid in motion, called Fluid dynamics.
Notes:
This motion is describe by two laws.
Law of conservation of mass gives us the equation of continuity.
Law of conservation of energy is the basics of Bernoulli equation.
19. Viscosity, Drag force, Stokes law
Viscosity:
The frictional force between layers of fluid is called viscosity.
It is denoted by Greek latter [η] “eata”.
Drag force:
Retarding force experience by object while moving through liquid.
F = 6πηrv
Which is called stokes law.
20. Terminal velocity
Definition:
When the magnitude of drag force becomes equal to the weight, the net force acting on
object zero. The constant speed at which it falls is called terminal velocity.
Vt = 2g𝒓 𝟐
ρ / 9η
21. Fluid flow
Streamline / steady / laminar flow Turbulent flow
Flow of fluid in which every particle
flow the same path and passes through
the same point.
Irregular flow of fluid is called is
turbulent flow.
22. Equation of continuity
Statement:
The product of cross sectional area of pipe and fluid speed at any point is constant. This
constant is equals to volume flow per second or simply flow rate.
Statement:
A1V1 = A2V2
23. Bernoulli’s equation
The sum of pressure, K.E per unit volume, P.E per unit volume is equals to constant.
P + ½ ρ𝒗 𝟐
+ ρgh = constant