Rotation Questions and Answers

3 25 Two blocks each of mass M are connected to the ends of a light frame as shown in figure 3 87 The frame is rotated about f the vertical line of symmetry The rod breaks if the tension in it exceeds To The maximum frequency with which the frame may be rotated without breaking the rod will be 71 2 A B C 1 To 2T MI 1 2 To MI 1 MT 2 1 2 10T 1 2 117 10 1 M 0 Figure 3 87 M Un

Three weights 20 gf 50 gf and 80 gf a re suspended from 10 cm 20 cm and 6 0 cm mark of a uniform metre scale of mass 60g Can you balance the scale a t 55 cm mark by using an additional ma ss of 100g If yes how if no why

A disc of radius R and thickness has moment of inertia R 48 about an axis passing through its centre and perpendicular to its plane Disc is melted and recast into a solid sphere The moment of inertia of the sphere about its diameter is 10 116 1 12

42 180 Mark for Review Which of the following statement is incorrect Moment of inertia is independent of distribution of mass about rotational axis Moment of inertia depends on orientation and position of axis of rotation Moment of inertia is independent of angular velocity of rotating body Flywheel resists sudden increase or decrease of speed of vehicle

48 A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity The force exerted by the liquid at the other end is 2006 a MLw 2 c 2MLw b ML w 2 d ML 2

1m and mass m 5kg is rolling On a plane surface a hollow sphere of radius R without slipping The centre of the hollow sphere is moving with a speed v 3m s on a straight line Determine the total kinetic energy of the hollow sphere A 3 45J B 35 5J

The potential energy U of two atoms of a diatomic molecule as a function of distance between the atoms is shown in the given figure Read the following statements carefully 1 The equilibrium separation distance between the atoms is equal to 12 2 At r the force between the atoms is repulsive 3 For r r the force between the atoms is attractive Which of the above statements is true

1 A coil having magnetic moment 15 A m placed in a uniform magnetic field of 4 T in the horizontal direction exists such that initially the axis of coil is in the direction of the field If the coil is rotated by 45 and the moment of inertia of the coil is 0 5 kg m then the angular speed acquired by the coil is a 20 rad s b 10 rad s c 8 34 rad s 1 d 4 5 rad s

2 9 A particle of mass m slides without friction on the inside of a cone The axis of the cone is vertical and gravity is directed downward The apex half angle of the cone is 0 as shown The path of the particle happens to be a circle in a horizontal plane The speed of the particle is to Draw a force diagram and find the radius of the circular path in terms of to g and 8

A rotating Rod on a Sleeve On a smooth rod PQ a sleeve A of mass m can smoothly slide and a thin uniform rod of mass m and length is hinged at one end which can rotate in the plane of figure on sleeve and kept in vertical position as shown in figure If system is released from rest find the velocity of sleeve when rod rotates by 180 angle P A m

Two rods AC and BC of equal length l are hinged together at end C The ends A and B are moving with the velocities 6 m s and 4 m s respectively along the horizontal surface as shown The velocity of the end C at this instant is 6 m s A O 60 m s 2 7 m s 04 4 m s 05 7 m s 60 B 4 m s

ghest poin 76 A small object placed on a rotating horizontal turn table just slips when it is placed at a distance 4 cm from the axis of rotation If the angular velocity of the turn table is doubled the object slips when its distance from the axis of rotation is a 1 cm b 2 cm c 4 cm d 8 cm 77 A particle is moving on a circular path of 10 m

A horizontal disc of mass M and radius R rotates freely about a vertical axis through its centre with angular velocity Aring of same mass M and radius R is now gently placed on the disc After some time the two rotates with a common angular velocity A some friction exists between the dise and the ring B the angular momentum of the disc plus ring is conserved about the mentioned axis of rotation C the final common angular velocity is o 3 2 D rd of the kinetic energy lost into heat

QUESTION A13 1 mark A 4 kg rod has a total length of 4 m and a pin O at the position shown G represents the centre of mass 1 5 m G question Do not post questions online Determine the angular acceleration of the rod a 2 05 rad s b 8 20 rad s c 4 10 rad s d 12 3 rad s e None of the above

A uniform rod of mass m and length L is free to rotate in the vertical plane about a horizontal axis passing through its end The rod is released from rest in the position shown by slightly displacing it clockwise Find the hinge reaction at the axis of rotation at the instant the rod turns through 90 degree and 180 degree

The angular momentum of a system of n particles about the origin is Where p is momentum r is the position Pi vector of the particle f is the force and w is the angular velocity 1 L n ri Pi 1 n 2 L ri fi 1 in 3 L 1 Pi fi

Example 9 15 Three rods each of mass m and length I are joinea to form an equilateral triangle as shown in figure Fina together the moment of inertia of the system about an axis passing through its centre of mass and perpendicular to the plane of the triangle BO A 0 CM

k 18 10 26 2 10 4 18 10 k 7 2 N m n 10 22 From a uniform circular disc of radius R and mass 9 M a small disc of radius is removed as shown in the R 3 of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is here on the f 1 10 MR 37 3 4 MR 2 MR 9 40 MR figure The moment 33

a bicycle is in motion the force of friction exerted by ground on two wheels is such he backward direction on the front wheel and in the forward direction on the rear w he forward direction on the front wheel and in the backward direction on rear whee the backward direction on both front and the rear wheels forward direction on both front and rear 1 2 3 iii iv ii iv

16 Seven identical circular planar disks each of mass M and radius R are welded symmetrically as shown The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is 73 1 MR 3 2 19 2 MR 2 4 181 2 55 2 MR MR2

The moment of inertia of a square plate about axis AB is I then moment of inertia about A B as shown in the figure will be B A A Isine Icose B

A hollow sphere and solid sphere rolls on a horizontal surface without slipping with same linear velocity If both has same mass and radius and total kinetic energy of hollow sphere is 15 J then total kinetic energy of the solic sphere is 63 53 J 30 J

Let current i 2 A be flowing in each part of a wire frame as shown in fig The frame is a combination of two equilateral triangles ACD and CDE of side 1 m It is placed in uniform magnetic field B 4T acting perpendicular to the plane of frame The magnitude of magnetic force acting on the frame is X X X C X X A X X X D X X E X X X X X X

and move A particle of same mass m moving on the plane with velocity v strikes the rod at pol making an angle 37 with the rod The collision is elastic After collision

The figure shows an overhead view of a ring that can rotate about its center like a merry go round Its outer radius R is 1 0 m its inner radius R is R 2 its mass M is 8 0 kg and the mass of the crossbars at its center is negligible It initially rotates at an angular speed of 8 7 rad s with a cat of mass m M 4 on its outer edge at radius R By how much does the cat increase the kinetic energy of the cat ring system if the cat crawls to the inner edge at radius R Number i Units

Two metallic cylinders A and B of radii 2r and 3r are joined as shown in figure If top end is fixed and lower end is twisted by an angle 0 then angle of twist for cylinder A is 1 3 116 15 0 81 0 97 l 2r A 3r 2 B 16 17 0 16 4 0

Five forces are applied to a uniform square a 2 0 m as shown where F1 2 C N F2 3 0 N F3 2 8 N F4 5 0 N and Fs 1 0 N Find the moment arm and the torque for each force applied at axes located at the vertices Each axis is orthogonal to the plane of the square B F24 a F3 O C F

nder with radius 12 m mass 9 kg and moment of inertial 2 7 kg m around its center is coming down a hill as shown in the picture without slipping The center of mass of the cylinder is at its center The cylinder starts at rest What is velocity of the center of the cylinder when its center s height is reduced by

4 A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity w The force exerted by the liquid at the other end is AIPMT Prelims 2006 1 MLw 2 3 MLw 2 4 ML w 2 ML w

Consider a rope of mass 4m and length 4 R on a fixed rough pulley of radius R as shown in the figure The rope is in equilibrium Length of vertical hanging parts is shown in the figure AR 2TR A Torque of tension force about O on pulley is mgR B Torque of normal force between rope and pulley on pulley about O is zero C Torque of friction force between rope and pulley on pulley about O is mgR D Torque of friction force between rope and pulley on pulley about O is zero

Two identical ladybugs sit on a rotating disk as shown in the figure The ladybugs small compared to the radius of the disk are at rest with respect to the surface of the disk and do not slip Ladybug 1 is halfway between ladybug 2 and the axis of rotation What is the ratio of the angular momenta of the two ladybugs with respect to the rotation axis L L 01 4 2 1 4 O 1 2

A system of two blocks A and B are connected by an inextensib The pulley is massless and frictionless Initially the system is at re moving with a velocity u as shown hits the block B and gets em

A tram is moving to the left at 6 m s and decelerating at 4 m s A 2m rotating rigid rod i attached to the bottom of the tram The rod is rotating counterclockwise with an angular velocity of 2 rad s and its angular speed is decreasing at 3 rad s At that time the rod is oriented 30 counterclockwise from the negative y axis as shown What is the absolute acceleration of the end of the rod Point B ac 4 m s 3 rad s2 L 2 m 30 Vc 6 m s w 2 rad s

A flanged bolt coupling consists of ten steel 0 5 in diameter bots spaced evenly around boat circle 14 in dianeter Determine torque capacity of the couping if the allowable shearing stress in the bolts is 6000psi

A square plate of mass 10 kg and side 20 m is moving along the groove with the help of two ideal roller massless connected at the corners A and B of the square as shown in the figure At the given instant of time during motion as shown in the figure the corner A is moving with velocity 16 m s downward Find the speed of corner D approximately A 32 5 m s B 16 5 m s C 8 5 m s D none 16 m s AG 20m 37 D B

7 Two coherent point sources s and s2 vibrating in phase emit light of wavelength The separation between the sources is 2 The smallest distance from s2 on a line passing through s2 and perpendicular to S1S2 where a minimum of intensity occurs is 72 12 a b 15 4 Two identical coherent c 2 N d 3 4

A circular portion of diameter R is cut out from a uniform circular disc of mass M and radius R as shown in figure The moment of inertia of the remaining shaded portion of the disc about an axis passing through the centre O of the disc and perpendicular to its plane is RR O 15 MR Cut out portion 2 7 MR 3 13 32 MR 3 4 MR2 8

5 3 A body of radius r and mass m is rolling horizontally without slipping with speed v It then rolls up a hill to a maximum height h If h 3 4 g what might the body be What is the body s moment of inertia Ans R 2

5 5 A wheel of radius R rolls without slipping along the x axis with constant speed vo Find the total distance covered by the point on the rim of the wheel during one complete revolution of the wheel Ans 8P

7 A boy is pushing a ring of mass 2 kg and radius 0 5 m with a stick as shown in the figure The stick applies a force of 2 N on the ring and rolls it without slipping with an acceleration of 0 3 m s2 The coefficient of friction between the ground and the ring is large enough that rolling always occurs and the P coefficient of friction between the stick and the ring is 10 2011 The value of P is Ground Stick

Identify the correct statement for the rotational motion of a rigid body a Individual particles of the body do not undergo accelerated motion b The centre of mass of the body remains unchanged c The centre of mass of the body moves uniformly in a circular path d Individual particles and centre of mass the body undergo an accelerated motion

5 Calculate the moment of inertia I and Iy and the product of inertia Iy with respect to shown in the Fig 4 Take b 30mm h 40mm t 5mm xiy axes for the composite section and 0 60 2 2 2 2 Fig 4

A uniform 255 N rod that is 2 m long carries a 225 N weight at its right end and an unknown weight W 0 5 m from the left end The system is balanced horizontally with the fulcrum is located 0 75 m from the right end What is W and the normal force fr the fulcrum 11 N 620 N W 140 N

218 Systems of In carbon monoxide molecules the carbon and the oxygen atoms are se of the centre of mass from the carbon atom is 1 0 48 A 2 0 51 A 4 0 69 A lemon erf vid beansier ole Consider a system of two identical particles One of the particles is at rest and the other has an acceleration F The centre of mass has an acceleration 10000 arit ylaudivdo 1 Zero 2 F sp of ovitician bole to the f 3 0 56 A 3 abrata en aagin to nam A 4 27 and placed on a frictic

base R 5 0 cm rolls uniformly and without slipping over a hori zontal plane as shown in Fig 1 8 The cone apex is hinged at the point which is on the same level with the point C the cone base centre The velocity of point C is v 10 0 cm s Find the moduli of 19 2 a the vector of the angular velocity of the cone and the angle it forms with the vertical b the vector of the angular acceleration of the cone 1 58 A solid body rotates with a constant angular velocity w 0 50 rad s about a horizontal axis AB At the moment t 0 200 Fig 1 8 the axis AB starts turning about the vertical with a constant angu lar acceleration po 0 10 rad s Find the angular velocity and angular acceleration of the body after t 3 5 s

Question No 40 A body of mass M and radius of gyration K is rotating with angular velocity w 31 f rad s The torque acting on it at t 1s will be O 4MK O 5MK

A disc of mass m and radius Ris rolling with angular speed w on a horizontal surface as shown in figure The magnitude of angular momentum of the disc about point P here vis linear speed of centre of mass of disc 6 O O mvR 2 3mvR 2 mvR

Question No 32 A body rolls down an inclined plane If its kinetic energy of translation motion is 50 of its total energy then the body is O Solid cylinder O Solid sphere Disc Ring

When a sphere of moment of inertia I about its centre of gravity and mass m rolls from rest down an inclined plane without slipping its kinetic energy is 1 10 1 2 mv 3 Io mv 4 10 my

A horizontal circular disk with mass m and radius 2r can rotate easily about its vertical axis of symmetry O A small boy with mass km starts in A when the system is at rest and runs along the outer edge of the disk At B he goes radially inwards to C and continues along a quarter cincle anc to D How big an angle has the disc turmed when the boy has returned to A You have to draw the free body diagram The answaer of the question is w 4 2mr 1 104