11th Class Physics Chapter 5 Circular Motion Short Question Answers

Tangential Velocity:-When an object moves along a circle with constant speed the magnitude of linear velocity of the object remains constant but its direction changes continuously from point to point.The direction of linear velocity is always along the tangent on any point of the circle.This linear velocity is know as the tangential velocity.It is denoted by V_t.Angular velocity:The angular velocity is rate  of change of angular displacement of an object moving along a circle.It is vector quantity and denoted by its direction is found out by right hand rule stated as follow:
Curl the fingers of right and around the rotation axis in the direction of rotation then the thumb points towards the direction of angular velocity  ^ɷ→is  represented by a line drawn parallel to the axis of rotation.

Definition:It is defined as the product of mass of particle and square of its distance from axis of rotation.It is denoted by I
I =mr²…………….. (1)
If the rigid body is made of n-particles then different particles are at different distances from axis of rotation.Thus:
I =m₁r₂+m₂r₂²……………m_nr²_n
Where m₁m₂+……………are masses of n particles at distances r₁r₂…………r_n from axis of rotation respectively.So equation (1) can be written as
I=ⁿ∑_i=1 m_i r_i²…………..(2)

According to the definition of angular momentum
L_ᵒ^→.=r^→×p^→
Its magnitude is given by
L_ᵒ=rp sinΘ……………. (1)
where Θ the angle between position vecteor r^→ and velocity of linear momentum p^→
Equation (1) can be written as :
L_ᵒ=mrv sinΘ ………. (2)
In case of circular orbital motion such as satellite of mass m’
revolving around the Earth in a circle  of radius r the angle between radius ‘r’ and tangential velocity ‘v’ is always 90^ᵒ .Therefore
L_ᵒ=mrv sin90^ᵒ
Hence L_ᵒ=mrv

Direction of Angular Momentum:-
As we know that teh angular momentum is defined by
L^→r^→×p^→
The angular momentum is a vector quantity.The direction of angular momentum L^→is perpendicular to the plane containing r^→ and p^→ as show in fig (b)
Its  direction is determined by right hand rule.If an object is rotating along certain axis then direction of L^→ will be along axis of rotation,the angular momentum is directed outward along the axis of rotation.
Direction of Angular velocity:Angular velocity is a vector quantity.Its direction also can be found by the right hand rule.Curl the fingers of the right hand around the rotation axis in the direction of rotation then thumb points towards the direction of angular velocity ‘w’as shown in fig.

:(a) We consider an object as artificial satellite which is put into an orbit around the Earth by giving a suitable tangential orbital velocity.The satellite is put into orbit by rocket and is held in an orbit by gravitational pull of Earth.Its centripetal acceleration is equal to the acceleration due to gravity directed towards the center of Earth.Therefore a satellite is always falling towards the center of Earth with an acceleration’. Hence the satellite is said to be free falling object.Due to the tangential velocity and downward velocity due to force of gravity it move along a curved path.The curvature of this path is such that the Earth Curves around by the same amount as the moving object and therefore does not touch the surface of earth.As the object continues to fall during its orbit around the Earth so it is said to be free falling.
(b) Whenever a frame of reference of free falling object is moving under gravity the weight of the body in that frame of reference will be zero.In other words it will be weightless.As the relative acceleration of an inside body with respect to its frame of reference is zero because both are falling together with the same acceleration.Therefore it appears weightless.
Hence if the satellite is in free fall all the objects inside it appear to be weightless.

The mud will fly off tangentially along a straight line.When the Tyre rotates a centripetal force acts on the mud which is equal to the adhesive force between the Tyre and mud.When the angular speed of the Tyre increases the centripetal force on the mud also increases.When this centripetal force is greater than the adhesive force the mud leaves the tyre and flies off tangentially along a straight line due to centrifugal force which is simply the reaction of the centripetal force.

A diver changes his body position to spin himself faster so that he may be able to take extra somersaults.For this purpose when the diver lifts off the diving board his legs and arms are fully extended in order to have a large moment of inertia l₁ about an axis.Thus his angular velocity ɷ₁ decreases.When he pulls his legs and arms into closed tuck position his moment of inertia is reduced to a new value I₂.So the value of his angular velocity ɷ₂ increases.As the angular momentum is conserved so
I₁ɷ₁=I₂ɷ₂= constant
Hence the diver spins faster when moment of inertia becomes smaller and angular velocity increases to conserve angular momentum.In this way he can make more somersaults.

The minimum number of geo- stationary satellites required for global coverage of T,V.transmission is 3.Since one geo- stationary satellite covers 120ᵒ of longitude so for the whole populated Earth’s surface there must be 360ᵒ of longitude.Hence the whole of Earth’s surface for global coverage of T.V. transmission can be covered by three correctly positioned geo- stationary satellites.

Centrifugal forces and the friction between the treys of the motor cycle and the vertical wall prevent the motor cyclist to fall.

The weight of a body in a certain frame of reference is a force which is equal and opposite to the force required to prevent it from accelerating in their frame.Therefore it will be weightless.It means that a freely falling body will have no weight.

The centripetal force does not do any work because this force is always acting at right angle to the motion of the body or to the velocity of the body along the tangent.Therefore,
Work =F^→.v^→=Fv cos90^ᵒ =0
Thus the work done by the centripetal force on the body is zero.

The plane has a downward acceleration greater than g.this may happen when a plane is diving.

To put a satellite into an orbit around the Earth it is given a suitable tangential orbital velocity.These bodies tend to fall freely due to gravitational pull of Earth.This means that the satellite the person and every object in the satellite are free falling bodies.Due to the tangential and downward forces these objects move along a curved path.The curvature of this path is such that the Earth curves around by the same amount as the moving object and therefore does not touch the surface.But the body continues to fall during its orbit around the Earth.This gives the feeling of weightlessness.As the person has no acceleration relative to satellite so he appears weightless.

As we know that the quantity mr2 is called the moment of inertia.The moment of inertia plays the same role in angular motion as the mass in linear motion.It may be noted that moment of inertia depends not only mass but also on r.Two cylinders are of equal mass but the rotational inertia also depends upon the radius.The one with the larger radius has the greater rotational inertia.Therefore the cylinder A will require more force to come into rotation.

When crow takes away a piece of bread the mass of bread on the rotating plate decreases and its moment of inertia also decreases.But since the angular velocity of the plate increases that is
I₁ɷ₁= I₂ɷ₂

It is the experimental fact that the gravitational acceleration decreases invesely as the square of the distance from the center of the Earth.The higher the satellite the slower with the required speed and longer it will take to complete one revolution around the Earth.Thus it is concluded that satellite will have different time period at different altitudes.

As we know that when elevator is moving downward the net force on the bodies is given by
W-T=F=ma
or   T=W-ma
The apparent weight is given by
W^/= T=W-ma
=mg-ma
W^/=m(g-a)……………..(1)
When the chain supporting the elevator breaks the elevator falls freely with an acceleration to ‘g’
Thus     a=g
Putting it in equation we get
W^/=T=m(g-g)=0
W^/=0
Hence the apparent weights of both the bodies inside the elevator is zero or the bodies seem to be weightless.It is the state of weightless.

Lead has greater density then copper.For the same mass the radius of lead sphere and hence its moment of inertia is smaller than a copper sphere.Therefore it will be easier to rotate a lead sphere.

At present the mass of Earth is more concentrated near the center so that the moment of inertia of Earth is smaller.If the mass of Earth is evenly distributed with uniform density then moment of inertia of Earth would become greater.According to law of conservation of angular momentum its angular velocity would decrease.Which means a day would become longer.

If the angle is measured in radians rather than in degrees then we can easily find out the length of the are which subtends this angle at the center of the cried, i.e.Length of the are =radius×angle in radians.
S=r Θ
This equation is valid only if angle Θ is measured in radians not in degrees r.As the angle used in S.I unit is in radians

Relation between degree and radian 1 radian = 57.3ᵒ 57.3ᵒ=1 radian 1ᵒ=1/57.3 2ᵒ=2/57.3=0.03 radian

No,these forces do not balance each other since they act on two different bodies according to third law of motion.When a body is moving in a circle the only force acting on the body is the inward centripetal force.The outward centripetal force is only a reaction force therefore they do not balance each other.

No the centripetal force does not do any work because this force is always acting at right angle to the motion of the body or to the velocity of the body along the tangent.
Therefore,  work=F^→.v^→=Fv cos 90=0
Therefore the work done by the centripetal force is zero.

No a body can never move in a circle without centripetal force because there must be a force which should compel the body to move in a circle.

When a car is turning round a corner the centripetal force acting on it is given by Fc=mv2/r Where m=mass of the car v= speed of the car R= radius of the curved path. It is clear from the above expression that the centripetal force acting on the car is directly proportional to the square of its speed.Thus at high speed the centripetal force acting on the car will increase and it will be harder to turn round a corner.

If a raw egg and a hard boiled one are rotated on a table with the same angular velocity the raw egg will continue rotating for a longer time and thus we can distinguish between them.The reason is that the mass particles of a hard boiled egg are fixed at their places while those of raw egg are free to move.When the two eggs are rotated the yolk of raw egg is displaced to its walls due to centrifugal force and moment of inertia of the egg increases while that of the boiled egg remains constant.That is why the raw egg remains spinning for longer time as compared to hard boiled egg and they can be distinguished.

If the body of mass ‘m’is taken to the Moon its weight is given W_m=mg_m =acceleration due to gravity of Moon.It has been found that acceleration due to gravity of Moon ‘gm’ is one sixth of the value of acceleration due to  gravity of earth ‘g’i.e.
gm=g/6
Therefore the weight of the body at the Moon will reduce 1/6 of its value on earth.

When the body is taken inside towards the center of the earth the value of ‘g’ goes on decreasing when the body reaches the center of earth the value of ‘g’ becomes zero i,e.
g=0
but W=mg
Here g =0
W=m×0=0
or W=0
Hence the weight of a body becomes zero at the center of the earth.

Suppose the elevator is descending with an acceleration ‘a’ it means that weight ‘w’ is greater than the tension ‘T’ on the body.Net force acting on the body =W-t=F
Or       W-T=ma
Or   T=W-ma =mg-ma=m(g-a)
Thus     T=m(g-a).

If we moves from equator to north pole or south pole then the value of acceleration due to gravity increases because the radius of earth decreases as we go from equator to either of poles.

It is defined as the product of mass of a particle and square of its perpendicular distance from the axis of rotation.It is denoted by I.
Mathematically it can be written as
I=mr²
Where  m is the mass of the particle and r is the perpendicular distance of particle from axis of rotation.
Its Uniy: The SI unit of moment of inertia is kgm².

The angular momentum of an object is defined as the cross-product of position vector r with respect to the axis of rotation and linear momentum p of an object. It is denoted by L. Mathematically it can be written as L=r×p.

Geo-stationary satellite is the one whose orbital motion is synchronized with the rotation of the earth.

Such satellites are useful for the following purposes. (i)Worldwide communication (ii)Weather observations (iii)Navigation (iv)Other military uses.

Artificial Gravity:We know that the astronaut orbiting around the Earth is in the state of weightlessness.There will be no force pressing him to any side of spacecraft.If the spacecraft is to stay in the orbit for a longer time this weightlessness crests a lot of problem for the astronaut while performing his duty in the spaceship.To overcome this difficulty an artificial gravity is created inside the spaceship so that the astronauts may perform their experiments efficiently as they do in the Earth’s gravity.

The break drums of vehicles are made of larger diameter so that greater rotational inertia may be produced.

The law of conservation of angular momentum has many applications from creation of stars down to subatomic particles. (i)Divers (ii)Ice skaters (iii) Ballet dancers (iv)Acrobats

The spin angular momentum is the angular momentum of a spinning body about its own axis.The orbital angular momentum of a body moving along a circular path.

A spaceship in an orbit is a freely falling bidy having an acceleration ‘a’ towards the center of Earth equal to the value of the acceleration due to gravity ‘g’ at the radius of the orbit.The apparent weight W^/ is expressed as
W^/=W-ma
Where W is its actual weight thus
W^/=mg-ma=m(g-a)
But in the case of free fall,a=g
Therefore W^/ =m (g-g)=0
Hence W^/=0
Thus the spaceship will be called weightless with the condition of falling freely with an acceleration a=g.

Banked tracks are needed for turns that are taken so quickly that friction alone cannot provide energy for centripetal force.

The energy due to the spinning of a body about its axis is called rotational kinetic energy.
Mathematically it can be written as
K.E._max=1/2 Iɷ²
Practical use of Rotational K.E.:This energy is put to practical use by flywheels which are essential parts of many engines.A flywheel stores energy between the power strokes of the pistons so that the energy is distributed over the full revolution of the crankshaft and hence the relation remains smooth.

Intelsat stands for International telecommunication Satellite Organization.Intelsat –Vi operates at microwave frequencies of 4,6,8.and 14 GHZ.

The weight of a body on the surface of the Earth has a constant value by the relation W=mg.There is possibility of changing the value of ‘g’ in the elevator moving up and down.Thus the weight in moving elevator will be different than measured on the surface of the Earth.This weight of the body measured in moving elevator is called its apparent weight.

When the car moves align a circular path acceleration a^→ is along the radius and velocity v ^→along tangent.Thus they become perpendicular to each other.It means that acceleration a^→ and velocity v ^→ have different directions.

It is human made satellite which orbits around the earth.It is put into orbit with help of racket.It is held in orbit by the gravitational pull of earth.

(i)Satellite orbiting the earth. (ii)The earth rotating about its axis. (iii)A spinning top (iv) The wheel of a car rotating on their axles.