## ^Sign of work

^Sign of work

1. Sign of work depends on sign of cosθ. As cosθ can be 0, +ve or – ve (recall –1 ≤ cosθ ≤ +1), hence the work done by a force also can be 0, + ve or – ve depending upon the angle between the force and the displacement.
2. Work done by a force acting at acute angles to displacement of a system is +ve.
3. Work done by a force acting at obtuse angles to displacement of a system is – ve.
4. +ve work increase the KE of the system.
5. – ve work decrease the KE of the system.

## ^Chain on a rough horizontal table

^Chain on a rough horizontal table

Fraction of chain length that can hang without slipping on a rough table is  ## ^Forces in circular motion

^Forces in circular motion

When seen from inertial frame two types of forces act is a circular motion, one that changes speed & the other that changes direction.

A force that acts tangential of velocity changes the speed only, called tangential force. Its

magnitude is given by A force acting normal to velocity towards turning centre, along the radius & changes direction is called centripetal force or radial force.

It is not a different type of force. It is actually the resultant of the forces acting on a system & directed towards the center of the circle. For planet revolving around sun gravitational force is centripetal. For a string whirled in a horizontal circle tension in the string is centripetal force. For oscillating pendulum resultant of tension in the string & normal component of weight is centripetal.

Example 1

The electrostatic force of attraction between electrons & nucleus changes the direction of electrons revolving around the nucleus thus we can write

FCP = Felctrostatic Example  2

Gravitational force of attraction between the moon & the earth changes the direction of moon thus we can

write, FCP = Fgravitational Example 3

Magnitude of centripetal force on a mass moving with velocity v in a circular path of radius r at constant speed (i.e. uniform circular motion) is  ## ^Block at rest w.r.t . accelerating wedge

^Block at rest w.r.t . accelerating wedge

Let complete system has acceleration a  w.r.t. ground

but the block (mass, m) is to

be kept at rest relative to wedge NSL for block + wedge is,

(M + m) a = F

To keep m at rest relative to wedge

ma cosθ = mg sinθ  or a = gtanθ

Thus the minimum horizontal force needed should

Be, F = (M + m) g tanθ

Also the normal pressing force exerted by wedge on block is, N = mgcosθ + masinθ = mg secθ

## ^Force, F

^Force, F

A push or a pull or an agent that breaks the inertia (tendency of opposition) changes its state from rest to motion or from motion to rest or from moving in one direction to other or accelerates it.

## ^Kinematics of circular motion

^Kinematics of circular motion

Suppose a particle is rotating anticlockwise in a circular path in xy plane. Its angular velocity vector at any point on circular path w.r.t. center is     ## ^Projectile thrown straight up

^Projectile thrown straight up

Suppose a body is projected upwards from the ground and with the velocity u. The characteristics of motion of such a body are as follows.

1. The maximum height attained 2. Time taken to go up (ascent) = Time taken to come down (descent) 3. Time of flight 4. For an object thrown straight upwards with u = 50 m/s\
5. 6. The speed of the body on return to the ground = speed with which it was thrown upwards
7. When the height attained is not large, that is u is not large, the mass, the weight as well as the acceleration remain constant with time its speed, velocity, momentum, potential energy and kinetic energy change with time.
1. Let m be the mass of the body. Then in going from the ground to the highest point, following changes take place.
• Change in speed = u
• Change in velocity = u
• Change in momentum = m u

Change in KE = Change in PE = 1. On return to the ground the changes in these quantities are as follows:
• Change in speed = 0
• Change in velocity = 2 u
• Change in momentum = 2 mu

Change in KE = Change in PE = 0

1. If the friction of air be taken into account, then the motion of the object thrown upwards will have the following properties:
• Time taken to go up (ascent) < time

taken to come down (descent)

• The speed of the object on return to the

ground is less than the initial speed. Same is true for velocity (magnitude), momentum (magnitude) and KE.

• Maxi height attained is less than .
• A part of the KE is used up in overcoming

the friction.

## ^Crossing a river

^Crossing a river

Suppose a person start rowing his boat from point O with velocity vbr (w.r.t. river i.e. without considering the effect of water) towards point S in order to cross a river of width ‘w’ flowing at a speed ‘vr’ towards x axis. Let under the effect of river current boat has net velocity the boat vb (w.r.t. ground i.e. resultant vbr & vr) & he reaches point R, then the distance SR covered downstream (i.e. distance along the stream) is called drift.  ## ^Geometrical optics

^Geometrical optics

Geometrical optics is also called ray optics. It treats propagation of light in terms of rays and is valid only if wavelength of light is much lesser than the size of obstacles. It deals with the following phenomena

1. rectilinear propagation (i.e. light propagates in a straight line, due to its small wavelength)
2. reflection (i.e. coming back in same medium on striking a shining surface)
3. refraction (i.e. change of speed on changing transparent medium)
4. dispersion (i.e. light splits up in to its constituent colours on changing transparent medium)
5. image formation ( i.e. intersection of two or light rays after undergoing reflection or refraction).

## ^What is optics?

^What is optics?

The branch of Physics which deals with light, it’s nature, cause, source, properties & it’s effects is called Optics.

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