1Q. Define angular displacement. What are its Units? A. Angular Displacement:the angle described by a radius vector of particle on a rotating body in a given interval of time is called angular displacement. Units
: Radians
2Q. Define angular velocity. What are its units? A. The rate of angular displacement is defined as angular velocity. Units:- radians / second. 3Q. Distinguish between rotatory motion and a circular motion. [Imp/2M] A. Rotatory motion 1.The motion of a particle under the action of a force always directed towards a fixed point away from its path is called Rotatory motion. 2. It is the characterised by changing linear velocity and radius vector.
Circular motion. 1 It is a special case of Rotatory motion.
2. In circular motion magnitude of velocity does not change while direction alone changes.
4Q. When do you say that a body is in uniform circular motion? A. If the magnitude of linear velocity of the particle remains constant but its direction changes continuously, then the body is said to be in uniform circular motion. 5Q. What is a Centripetal acceleration? A. A particle executing uniform circular motion undergoes a continuous change in the direction of its velocity which results in an acceleration directed towards the centre of the circle called centripetal acceleration.
2 6Q. What is a centripetal force? A. The force which acts continuously on a particle initially moving with a linear velocity and makes it travel along a circular path is called centripetal force. 7Q. What is the direction in which sparks fly when a knife is pressed on a rotating grind stone to sharpen the knife ? A. The sparks fly tangential to the circular grinding stone. 8Q. Distinguish between inertial and non-inertial frames of reference. A. Inertial frame of reference
Non-Inertial frame of reference
1) An imaginary co-ordinate system which is either at rest or in uniform motion and where Newton’s laws are valid is called an Inertial frame of reference.
1) An imaginary co-ordinate system which is attached to a rotating or accelerated body Newton’s law are not valid is called non-inertial frame of reference.
9Q. Distinguish between centripetal and centrifugal force. [V.Imp] A. Centripetal force 1. It acts normally on a particle executing a uniform circular motion. 2. It is directed radially towards the centre of the circle. 3. Its magnitude is F = mv2 r = mrw2 4. It is associated with External agent. 5. It is a real force in an inertial frame of reference. 6. It is pull on the body towards the centre of the circle. 7. It is necessary to make a body to travel on a curved path. 8. In a uniform circular motion, its Magnitude is constant. 9. Centripetal force depends on mass of a body in a circular Motion with speed V.
Centrifugal force 1. It acts normally on a particle executing uniform circular motion. 2. It is directed radially away from the centre of the circle. 3. Its magnitude is F = mv2 r = mrw2 4. It cannot be associated with any agent. 5. It is a fictitious force in an Inertial frame of reference. 6. It is a tendency of the body to fly away from the centre of the Circle. 7. It comes into play in a rotating frame of reference. 8. In a uniform circular motion its Magnitude is constant and equal to that of the centripetal force. 9. It is depends on mass of the body. Hence bodies of higher mass rotate on a circle of higher radius.
3 10Q. Why is Centrifugal force called a fictitious force? A. Centrifugal force cannot be associated with any object. So it is called a fictitious force. 11Q. What is Centrifuge? How does it work? [V.IMP] A .Centrifuge:- It is a machine used to separate particles of higher mass from those of lower mass in a given mixture. i) It works on the principle “The bodies of higher mass rotate on a circle of higher radius. ii) It consists of a cylindrical vessel rotated about it own axis at high speed with the help of an electric motion. iii) When milk is poured into cylindrical vessel and rotated at high speed, the particles of higher mass are thrown away. iv) The particles of lower mass are collected at the centre i.e., near the axis. 12Q. Explain the working of a laundry drier? [V.IMP./2m] A. (i) Laundry drier is used to dry the wet clothes. (ii) It works on the principle, ‘The bodies of higher mass rotate on a circle radius’. (iii) It consists of a cylindrical vessel containing holes. (iv) Wet clothes are dropped into the vessel and it is rotated at high speed. (v) Wet clothes get struck to the vessel and centrifugal force pushes the water molecules through the holes. (vi) Thus clothes are dried. 13Q. What is the necessity for banking of roads? [IMP/2m] A. When a vehicle moves on a curved road the necessary centripetal force is provided by the frictional force between the wheels and the road. If this frictional force is not sufficient, the vehicle may skid. Hence Banking of the roads is necessary. 14Q. What is banking angle? A. The angle made by the line joining the outer raised edge of the road to the inner edge with the horizontal line is called banking angle. 15Q. What is the principle of launching a satellite into an orbit? [V.V.IMP/2m] A.The principle of launching an artificial satellite into a proper space orbit is to impart sufficient initial horizontal speed such that it revolves round the earth at the chooses height. II. Solve the following problems. (1) An object is moving along a circle of radius 6m with a constant speed of 12 m/s. Calculate its angular velocity. Sol:-Radius of the circular path (r) = 6m Speed of the object v = 12m/sec. Angular velocity w=v r = 12 6 = 2 radius/sec.
4 (2) The speed of a wheel is 1800 r.p.m. Find its average angular velocity in Radius/Sec. [IMP.] Sol:-Speed of wheel = 1800 rpm Period of revolution of the wheel = 60/1800 = 1/30 Angular velocity w = 2 π = 2 π T 1 30 2 π * 30 = 60 π = 60 * 22 7 ⇒ 8.57*22 = 188.54 radius / sec. 3Q. What is the angular velocity of the earth about its own axis. [IMP] Sol:- Period of revolution of the earth = 24 hrs. = 24*60*60 = 86400 sec. Angular velocity w = 2 π 2 π rad./sec. T = 86400
4Q. A curved road of 100m radius is banked with an angle of 10º. Find the safe velocity for a vehicle moving on the road. A. Radius of curved path r = 100m Angle of banking θ = 10º Acceleration due to gravity g = 9.8m/sc2 Let safe velocity = v But tan θ = v2/rg ⇒ Tan 10º = v2 100* 9.8 V2 = 980*0.1763 V2 = √980*0.1763 ( ∵ Tan 10º = 0.1763 V
= 13.14 m/sec.
III. Fill in the blanks:(1) Circular motion is a special case of rotatory motion. (2) If the string of whirling stone is cut, the stone moves in Tangential direction. (3) In a uniform circular motion angular velocity is constant. (4) Centre seeking force is called centripetal force. (5) Newton’s laws are valid in Inertial. (6) Centrifugal force means fictious force. (7) In a uniform circular motion, if the radius is doubled, the centripetal force now required is half as great as before. (8) A car of mass 1200 kg takes of a curved road of radius 180m with a Speed of 6 m/s. The centripetal force acting on the car is 240N. (9) A car moves on a curved but level road. The necessary Centripetal force on the car is provided by Friction between the tyres and the road .
5 separate the particles of higher
(10) The device used to mass from those of lower mass in a given mixture Centrifuge. IV. Match the following :1) Angular displacement [B] (A) Centrifugal force 2) Angular velocity [C] (B) radian 3) Fictitious force [A] (C) radians/sec 4) Banking angle [E] (D) Centripetal force 5) Centre seeking force [E] (E) banking of roads 4.3 Simple Harmonic Motion
1Q. What is a Periodic Motion? Give an example? A. (1) Any motion that repeats itself along the same path in equal intervals of time is called a Periodic Motion. (2) Examples:-(i) The motion of a Pendulum of a Wall Clock. (ii) Motion of strings in Musical Instruments. NOTE:The time taken for one oscillation is known as its Time Period. 2Q. When does a Periodic Motion? A. When a particle in a Periodic Motion moves back and forth over the same path, its motion is said to be oscillatory or vibratory motion. Hence every Periodic Motion is not necessarily an oscillatory motion. 3Q. Give examples for oscillatory motion observed in your day-to-day life. [IMP. 1 mark] A. (i) The motion of a pendulum of a wall clock. (ii) Motion of things in musical instruments like violin, guitar, etc. (iii) The invisible motion of atoms in a solid. (iv) Motion of mass attached to a spring. 4Q. What is a Simple Harmonic Motion? What are its characteristics? [IMP. 2M] A. Simple Harmonic Motion(SHM):- The to and fro motion of a particle about a mean position on a fixed path such that the acceleration of the particle is always directed towards the mean position and directly proportional to the displacement of the particle from its mean position is called a Simple Harmonic Motion (SHM). The characteristics of SHM are:(i) The motion of the particles is vibrating about a mean position. (ii) The acceleration of the particle is always directed towards the mean position. (iii) The magnitude of the acceleration (a) is directly proportional to the displacement (x) of the particle from its mean position a ⍺ (-x). 5Q. Are all vibratory motions SHM ? Justify your answer. A. All vibratory motions need not be simple harmonic motions. A vibratory motion becomes X.H.M. only if it satisfied the following properties. (i) The motion of particle is vibratory about a mean position. (ii) The acceleration of the particle is directed towards the mean position.
6 acceleration is directly proportional
(iii) The magnitude of to its mean position i.e. a ⍺ (-x) .
6Q. Describe an experiment to determine acceleration due to gravity by a Simple Pendulum ? [IMP. MARCH 2000] A. (1) A Simple Pendulum is arranged to a retort stand, note its length. (2) Place a pointer at the mean position ‘O’ in front of the bob. (3) Pull the bob a side and leave it, it begins to execute SHM. (4) When the bob comes left and is about to move right crossing the pointer Switch on the Stop Watch. (5) Count 20 Oscillations and note the time taken for 20 oscillations. (6) Repeat the experiment 3 times and note the time. (7) Take average of three values and find time period. (8) Repeat the experiment for different length and find l /T2 value. Sl.no.
l cm.
Time taken for 20 oscillatons 1st time 2nd time
Average Time time(sec) period(sec)
T2
3rd time
7Q. Find length of a Simple Pendulum whose time period is 1.2 sec. Given g=9.8m/s2. Sol. Time Period T = 1.2 sec. Acceleration due to Gravity g = 9.8m/s2 But g = 4π 2 l /t2 l = g * t2 4π 2 l = 9.8*1.2*1.2 4*22/7*22/7 l =
35.7 cm.
8Q. In a Simple Pendulum experiment the value of l 2 / t2 is found to be 0.248m/s2. Find the value of ‘g’ at that plate. Sol. The value of l T2 = 0.248 Acceleration due to gravity ‘g’ = 4π2
l {T2 }
g = 4*22/7*22/7*0.248 g = 9.8 m/sec 2 II. Fill in the blanks: (1) Any motion that repeats itself along the same path in equal intervals of time is called Periodic .
l T2
7 (2) Periodic motion is also called as Harmonic Motion . (3) If a particle in periodic motion moves back and forth over the same path, its motion is called Vibratory Motion . (4) A body executing oscillatory motion comes to rest at Mean Position. (5) In a SHM, the acceleration of the particle is directly proportional To amplitude . (June 2002)
