Circular Motion Questions and Answers

8 Figure 11 27 shows an overhead view of a rectangular slab that can spin like a merry go round about its center at O Also shown are seven paths along which wads of bubble gum can be thrown all with the same speed and mass to stick onto the stationary slab a Rank the paths according to the angular speed that the slab and gum will have after the gum sticks great est first b For which paths will the angular momentum of the slab and gum about O be negative from the view of Fig 11 27 Figure 11 27 Question 8 2 1 4 5 6

A point P on the trajectory of a projectile projected at angle 0 with horizontal subtends angle a and B at the point of projection and point of landing then AL ja 1 tane tana tan 3 tane tan tano P B i 2 tana tan tane 4 tane tana 2tan

F ALLEN The length of a second hand in a watch is 5 1 cm Magnitude of change in velocity of tip in 15 second is 1 0 cm s 2 7 3 30 cm s cm s 30 2 2 30 An isotropic stationary source is emitting waves 6 cm s 4 f tip n 1 0 cm s H 3 30 cm s da 2 1 cm 15 403 30 2 2 2 30 cm s cm s feet in fi

If velocity of a particle is given by v 2t 3 m s 2 then average velocity in interval 0 t Is is 2 2 m s 3 4 m s 4 5 m s A particle of mass m 5 units is moving with a 3 3 m 2t 3 m s fan al a 0 1 s 1 3 4 m s m s m 2 m s 2 4 5 m s YX 4

A plane is revolving around the earth with a speed of 100 km hr at a constant height from the surface of earth The change in the velocity as it travels half circle is RPET 1998 KCET 2000 b 150 km hr d 0 a 200km hi c 100 2 km hr

On a smooth surface formed by revolving y f x about y axis a particle is kept at a position x y and is made to move in a horizontal circle of radius x with speed v under gravity It is seen that for a different value of x on the surface its speed v required to perform the circular motion is the same The va enx equation of curve is in formy Find a g Y X

A bead can move on circular wire of radius R as shown in figure It is attached by an inextensible thread which is being pulled horizontal with constar velocity v Find tangential and normal acceleration as a function of 0 02N 008 1 2 v an cos2 R aN v sin 77 0 4 2 R

A stone of mass 5 kg is tied to a string of length 2 5 m is whirled round in a horizontal circle What is the maximum angular velocity with which the stone can be whirled around if the string can withstand a maximum tension of 1250 N O 30 30 rad s O O 10 rad s 20 rad s 5 rad s

A particle is moving with a uniform speed vina circular path of radius r with the centre at O When the particle moves from a point P to Q on the circle such that ZPOQ 0 then the magnitude of the change in velocity is a 2v sin 20 c 2y sin b zero d 2vcos

A ball is projected with horizontal velocity vo 9gR at the bottom most point attached with inextensible string of length R fixed at O as shown Tension in the string when it is in horizontal position R

small block slides down from rest at point A on the surface of a smooth cylinder as shown At point B the block falls off leaves the cylinder The equation relating the angle and 0 is given by O sin 0 sin 0 Osin0 sin 0 cose cos 3

b A cord is wrapped around a wheel in Fig 1 which is initially at rest when 0 0 If a force is applied to the cord and gives it an acceleration a 7t m s where t is in seconds determine as a function of time a the angular velocity of the wheel and b the angular position of line OP in radians 5marks 0 2 m

A rod of length I can rotate freely in a horizontal plane about vertical axis 00 passing through one of its ends with angular velocity The mass per unit length linearly increases from A to 2A from the axis of rotation to other end as shown in the figure Find the tension in Newton in the rod at the middle point takeo 2rad sec 4 kg 3 l 3 6 meter and neglect the gravity

The shown H shaped apparatus contains an ideal incompressible liquid and has dimensions as shown in the figure The diameters of the tubes are small as compared to h and R The apparatus is rotated with a constant angular velocity about a symmetric vertical axis as shown in the figure The pressure at point A A may be more than Patm C may be equal to Patm B may be less than Patm D None of these CODOLOMHAMNA 3 R CILICILI

4 The bob of a 0 2 m long pendulum describes an arc of circle in a vertical plane If the tension in cord is 3 times the weight of the bob when cord makes an angle of 30 to the vertical then acceleration of bob in that position is 1 g 2 2 3g12 3 g 4 g

ar charge exist in A 1 58 A semi infinite insulating rod has linear charge density The electric field at the point P shown in figure 1 418 is 22 4 or 22 4 TE Figure 1 418 at 45 with AB B at 45 with AB D 22 4 r 22 at 45 with AB at 135 with AR

A motor cyclist to be treated as point mass is to undertake horizontal circles inside the cylindrical wall of a well of inner radius 4m Coefficient of the static friction between the tyres and the wall is 0 4 Calculate the minimum speed and frequency necessary to perform this stunt Use g 10m s

2 A truck is traveling along a curved path with a speed v 4 m s If its normal acceleration an 5 m s that has radius p 15 m determine the radius of curvature of the path and the magnitude of its acceleration if tangential acceleration at 2 m s 2 Marks

The traditional weapon known as the Bola can be used for hunting It consists of a set of weights at the end of ropes It is used by swinging the weights in uniform circular motion above your head prior to flinging it at your prey We will consider a simplified model of a bola as shown in the figure on the right Here we have one sphere of mass m 1 33 kg attached to the end of a rope of length L 0 79 meters At the time shown the person is swinging the mass at high speed so that the angle 8 78 3 degrees Calculate all the following The radius of the circle R The tension in the rope T The velocity of the mass v 8 PARAPR meters Newtons m s

which rotates at constant angular frequency as shown in the figure The mass moves with steady speed in a circular path of constant radius a is the angle string makes with the vertical Which of the following graph is correct 1 Vcos a OM Q Vcos a 2 A IN Vcos a 3

44 A body is projected vertically upward from ground If we neglect the effect of air then which one of the following is the best representation of variation of speed v with time t h 3 i 2

Ab inch circular power saw rotates at 5 100 revolutions per minute Round your answers to two decimal place a Find the angular speed of the saw blade in radians per minute rad min b Find the linear speed in feet per minute of one of the 24 cutting teeth as they contact the wood being cut ft min

A bicycle pedal is pushed by a foot with a 60 N force as shown The shaft of the pedal is 16 cm long Find the magnitude of the torque about P Enter your answer in N m Round your answer to one decimal place 60 N 70 10

d of 21 8 m s around a circular track which has a ra Why the car is accelerating even though its speed is constant 6105 an onlukk bust art to ytibolev gnitluzen ariszi terW 1269 or 01 am 25 a to vre alm 81 to vspolov isitini no d b Calculate the acceleration of the car c Calculate the time for the car to go around the track once T the period d Calculate the force of friction that is keeping the car moving in a circle e If the truck were to now drive on a circular track with a smaller radius how would the force of friction change Would it be more than less than or the same as the force in part d Explain your reasoning f Using the diagram below which is looking down on the track as the car moves clockwise Draw the direction of the rider s acceleration at the three shown points Label a Draw the direction of the rider s velocity at the three shown points Label v i ii

22 A turntable spins with an angular speed A bug of mass m begins walking slowly from the center toward the rim of the turntable Which of the following represents the maximum distance from the center that the bug can stand without slipping 1 8 a W b 1 80 60 c d g mar Bug

The arc from point a to the North Pole of a planel sublends a central angle for 45 as shown in the figure to the right the radius of the planet is 3550 miles any point on the surface of the planet except at the poles makes one revolution two pi radians about the axis of the planet in 20 hours where are the angular and linear velocity is her appointment with respect to its rotation around the axis of the planet planet Point A North Pole 45 3550 mi

A small plane makes a complete circle with a radius of 4 500 m in 90 seconds What is the centripetal acceleration of the plane O22 meters per second squared 5 0 meters per second squared 16 meters per second squared O 50 meters per second squared

A wheel turning 4 50 rad s experiences an angular acceleration of 0 822 rad s 2 What is its angular velocity after 12 0 s Unit rad s Remember CCW is CW is 1 rev 2 pi rad

4 A coin is placed 17 0 cm from the axis of a rotating turntable of variable speed When the speed of the turntable is slowly increased the coin remains fixed on the turntable until a rate of 43 0 rpm is reached at which point the coin slides off What is the coefficient of static friction between the coin and the turntable

7 A roller coaster at an amusement park has a dip that bottoms out in a vertical circle of radius r A passenger feels the seat of the car pushing upward on her with a force equal to six times her weight as she goes through the dip If r 22 5 m how fast is the roller coaster traveling at the bottom of the dip m s

5 A 3 60 kg object is tied to a 1 20 m long string and whirled in a vertical circle at a constant speed of 4 40 m s What is the tension in the string when the stone passes by the lowest point IN

11 You are riding a roller coaster going around a vertical loop on the inside of the loop If the loop has a radius of 56 0 m how fast must the cart be moving in order for you to feel 3 5 times as heavy at the bottom of the loop m s

A turntable is rotating at a constant angular speed of 36 revolutions per minute The radius of the turntable is 10 centimeters A 0 30 gram bug starts walking slowly from the center toward the rim of the turntable The coefficient of static friction between the bug and the turntable is 0 116 a Find the magnitude of the force of static friction b Find the maximum distance in centimeters from the center of the turntable that the bug can walk without slipping BL ar 0 36 rpm

35 A particle is moving with constant speed v in xy plane as shown in figure The magnitude of its angular velocity about point O is 1 3 YA 0 b V a b vb a 0 2 4 V b V X A

2 A 1 200 kg car drives at a constant speed around a circular track The coefficient of kinetic friction between the tires and the surface is 0 30 the height h of the car is 0 50 m and the tread G is 1 40 m If the angular velocity of car is 0 20 rad per second compute the radius of the track

Q1 A frictionless track ABCDE ends in a circular loop of radius R A body slides down the track from point A which is at height h 5 cm Maximum value of R for a body to complete the loop successfully is 5 cm A a 2 cm 10 b cm 3 15 c cm 4 18 d cm E B R C

Q 138 A boat travelling with a speed of 30 m s Q 13830 m s 40 m 50 m Rails and a toward centre of a whirlpool of radius 40 m at a distance of 50 m from the centre of the whirlpool What should be minimum velocity of the wind hitting its sails to avoid the whirlpool 1 36 m s 2 24 m s 4 20 m s 3 18 m s TA 1 36 m s 3 18 m s 2 24 m s 4 20 m s

E An electric fan rotating at 1200 rpm is switched off If the fan stops after 10 seconds the number of revolutions completed by the fan before it stops is assume uniform retardation 2 790 1 100 anolfasuo eq 2 50 gigo 0 Xos Zoover m 4 20 200

17 A cube of mass M starts at rest from point 1 at a height 4R where R is the radius of the circular track The cube slides down the frictionless track and around the loop What is the force in N which the track exerts on the cube at point 2 M 0 2 kg 4R R

A rigid body rotates with a constant angular acceleration of 4 0 rad s2 If wheel start from rest then the number of revolutions it makes in first 8 s will be nearly 1 15 3 10 2 20 4 25

2 A particle of mass M moves in a circular orbit of radius r around a fixed point under the influence of an K where K is a constant If the potential energy of the particle is zero at an infinite attractive force F 3 distance from the force center the total energy of the particle in the circular orbit is B C 0 K D 2 A K r 2 of ma00 otto K 2r 73

A small ball of mass m moving with speed v 2gL undergoes an elastic head on collision with a stationary bob of identical mass of a simple pendulum of lenght L The maxium height h from the equilibrium position to which the bob rises after collision is L

2 20 A mass m 0 4 kg is attached to a vertical rod by means of two strings of equal length I 2m The system rotates about the axis of the rod with 4 rad sec as shown If T is the tension in the upper string and T is the tension in the lower string then A T T A BU 0 B T 10 4N T 2 4N 60 T C T 3N T 10N D T T 4N

PHY A particle is moving along circular track with constant speed V If ratio of magnitude of average TR velocity to average speed after time t is 3v b 22 then value of a b will be take 7

A particle is moving along circular track with constant speed V If ratio of magnitude of averag 22 2 7 1 velocity to average speed after time t TR is 3v b then value of a b will be take

The figure shows a potentiometer arrangement D is the driving cell and C is the cell whose emf is to be determined AB is the potentiometer wire and G is galvanometer J is sliding contact which can touch any point on AB Which of the following are essential conditions for obtaining balance NARAYA A D ACADEMY A The emf of D must be greater than the emf of C B Either the positive terminals of both D and C or the negative terminals of both D and C must be joined to A C the positive terminals of D and C must be joined D The resistance of G must be less than resistance of AB

A bomb explodes on falling on a horizontal floor Dif ferent parts of the bomb are scattered in different direc tions each with velocity u Find the area of the floor which is littered by the fragments u g

Q 18 At the highest point a projectile has a only vertical component of velocity only horizontal component of velocity both a b either a or b depending on the magnitude of maximum height b c d

The particle P starts from rest at point U at time t 0 and then undergoes a constant tangential ac celeration a as it negotiates the circular slot in the counterclockwise direction Determine r r 0 and e as functions of time over the first revolution P X

A car is moving on a curved road of radius R The road is banked at an angle 9 The coefficient of friction between tyres of the car and road is u The minimum safe velocity on this road is NCERT I XI Pg 104 1 2 3 4 gR u tane 1 tano gR tan0 V 1 tane gR tan0 V 1 tane gR tan0 1 utane