Rotation Questions and Answers

An impulse J is applied on a ring of mass m 3 along a line passing through its centre O The ring is placed on a rough horizontal surface The linear velocity of centre of ring once it starts 3 rolling without slipping is v 2 1 2 OVERW 2 J 2m J J FX J max J m

A plank of length 2L leans against a vertical wall It starts to slip downward without friction The top of the plank loses contact with the wall when it is at a height of of its initial height 4 B half of its initial height th C A D of its initial height of its initial height 21

e I C Figure II 14 A uniform square plate is placed on a horizontal floor When it is given an angular velocity about a vertical axis through one of its corners as shown in figure I it takes time t to come to a complete stop Now the same square plate is given the same angular velocity to rotate about another vertical axis through its centre as shown in figure II How long will it take to come to a complete stop now a t 2 c 31 12 b 2t 3 d 2t

Q 39 Forces F F and F acts along sides of equilateral triangle as shown If torque about poin O is zero then F will be A F3 A F C A 2 F F C F F F F F B 2 D 2F 3F

A horizontal rod of mass M and length L is tied to two vertical string symmetrically as shown in the figure One of the strings at end Q is cut at t 0 and the rod starts rotating about the other end P Then P 1 At f 0 angular acceleration of rod about P 3g is 2L 2 At t 0 angular acceleration of rod about C M of rod is 3g 2L 3 At t 0 acceleration of C M of rod is downward direction to Younas 3g 4 in

of mass m is released from the state of rest over a large smooth solid sphere of mass M and radius R at rest on a smooth horizontal surface The particle strikes the sphere perfectly inelastically as shown in the figure Q 111 The speed of sphere just after collision is 5m 6gh A 4 M m 2M 5m C 3m 6gh 4 M m 2M 5m R 2 Q 110 Choose the correct statement A Momentum of the system M m is co served in horizontal direction B Momentum of the system M m is conserved in vertical direction C Net impulsive force on m will be zero D Net impulsive force on M will be zero B m E D h m 6gh 4 M m 2M 5m 2 m 6gh 2 M m 2M 5m

131 Which of the following is true about the angluar momentum of a cylinder rolling down a slope without slipping 1 Its magnitude changes but the direction remains 132 same 2 both magnitude and direction change 3 only the direction change 4 neither change A sphon 11 11

Obtain an expression relating the torque with angular acceleration for a rigid body

S Signals in form of light pulses are fed at one end of an optical fibre of circular cross section of radius r All the rays from the source lie within a cone of half angle measured from the axis of the optical fibre The refractive index of the material of the fibre is u A light pulse lasts for a duration rand two pulses are separated by a time interval At from each other What can be the maximum length of the fibre so that the output pulses are still distinguishable Al Light Pulser

Four masses are fixed on a massless rod as shown in figure The moment of inertia about the axis P is about 5 kg 2 kg 2 kg 5 kg 0 2 m 0 2 m 0 2 m 0 2 m 1 2 kg m 121 0 5 kg m P 2 4 1 kg m 0 3 kg m

of inertia of the system about an axis along the me Two rings having the same radius and mass are placed such that their centres are at a common point and their planes are perpendicular to each other Find the moment of inertia of the system about an axis passing c through the centre and perpendicular to the plane of one of the rings M mass of each ring and R radius a sphere about its diameter is 2 5 MR2 What is its moment of inertia about an axi

A cubical box of side a sitting on a rough table top i pushed horizontally with a gradually increasing force unti the box moves If the force is applied at a height from the table top which is greater than a critical height H the box topples first If it is applied at a height less than H the box starts sliding first Then the coefficient of friction between the box and the table top is KVPY 2009 a c a 2H H b d 2H a H a d

RT0102 03 A solid sphere is rolling down on inclined plane from rest and a rectangular block of same mass is also slipping down simultaneously from rest on a similar smooth inclined plane 1 both of them will reach the bottom simultaneously 2 the sphere will reach the bottom first 3 the rectangular block will reach the bottom first 4 depends on density of material BT0103

6 The motion of a particle is described by the equation x a bt2 where a 15 cm and b 3 cm sec Its acceleration at time 3 sec will be 1 36 cm sec 3 6 cm sec 2 18 cm sec 4 32 cm sec

35 A uniform rod of length 6L and mass 8m is pivoted at its centre C Two masses m and 2m with speed 2v and v as shown strike the rod and stick to the rod rest Due to impact if it rotates with angular velocity o then o will be Initially the rod is at MHT CET 2019 A 8v 6L B 1lv 3L C D zero

2 A solid sphere and a hollow sphere both of same mass and same radius are hit by a cue at a heighth above the centre C In which case Solid sphere Fig 12 110 a linear velocity will be more b angular velocity will be more c rotational kinetic energy will be more Hollow sphere

The moment of inertia of a disc is 5 x 10 4 kg m It is rotating freely about a vertical axis passing through its centre at a speed of 40 rpm A piece of wax of mass 20 g is attached at a distance of 8 cm from its centre Cal culate its new speed 911700 32 rpm

The figure shows an isosceles triangular plate of mass M and base L The angle at the apex is 90 The apex lies at the origin and the base is parallel to X axis A M The moment of inertia of the plate about the z axis is ML 12 ML2 6 X o ML 24 D none of these B

16 RT0015 The curve for the moment of inertia of a sphere of constant mass M versus distance of axis from its centre 1 3 V X 2 4 X 2 RTOO f mass M

A uniform disc of mass m and radius R is given a linear speed vo and a reverse spin such that its angular speed is 2wo as shown in the figure If v and a represent the linear and angular speeds of the disc when it starts pure rolling on the ground then 2 A v v Roo 3 C w 2 3R Vo Rwo 2 B v V Roo V 2 D D vo Rwo 3R m R 2wo rouk

A simplified model of a bicycle of mass M has two tires that each comes into contact with the ground at a point The wheel base of this bicycle the distance between the points of contact with the ground is w and the centre of mass C of the bicycle is located midway between the tires and a height h above the ground The bicycle is moving to the right but slowing down at a constant rate The acceleration has a magnitude a Air resistance may be ignored 40 W Assuming that the coefficient of sliding friction between each tire and the ground is u and that both tire are skidding sliding without rotating Express your answer in terms of W h M and g 41 What is the maximum value of u so that both tires remain in contact with the ground A W 2h C 2h W B h 2W D W h C What is the maximum value of a so that both tires remain in contact with the ground Wg Wg A 2h h hg 2W C B D h 2Wg h

75 A sphere starts rolling down an incline of inclination 0 Find the speed of its centre when it has covered a distance l 6 A hollow sphere is released from the top of an inclined plane of inclination 0 a What should be the minimum coefficient of friction between the sphere and the plane to prevent sliding b Find the kinetic energy of the ball as it moves down a length on the incline if the friction coefficient is half the value calculated in part a

The uniform solid block shown in figure has mass M and edge dimensions a b and c Calculate its rotationa inertia about an axis passing through one corner and perpendicular to the large faces on

directions 7 A rectangular rigid fixed block has a long horizontal edge A solid homogeneous cylinder of radius R is placed horizontally at rest with its length parallel to the edge such that the axis of the cylinder and the edge of the block are in the same vertical plane as shown in figure there is sufficient friction present at the edge so that a very small displacement cause the cylinder to roll of the edge without slipping Determine OTR a the angle through which the cylinder rotates before it leaves contact with the edge b the speed of the centre of mass of the cylinder before leaving contact with the edge and c the ratio of the translational to rotational kinetic energies of the cylinder when its centre of mass is in horizontal line with the edge

The 8 lb hoop I mr2 is given an initial angular velocity as shown The coefficients of friction between the hoop and surface are us 0 3 and 0 2 Part a Determine the angular velocity and velocity of the center of mass after 0 3 seconds Part b Determine the angular velocity and velocity of the center of mass after 3 seconds wo 6 rad s 6 in

23 A box of mass 1 kg is mounted with two cylinders mass 1 kg and moment of inertia 0 5 kg m2 and radius Im as shown in figure Cylinders are mounted on their control axis of rotation and this system is placed on a rough horizontal surface The rear cylinder is connected to battery operated via a belt as shown If sufficient friction is present between motor which provides a torque of 100N m to this cylinder cylinder and horizontal surface for pure rolling find acceleration of the vehicle in m s2 Neglect mass of motor belt and other accessories of vehicle a 20 m s c 15 m s Electric motor b 5 m s d 10 m s

3 42 Four particles each of mass m are placed at the corners of a square of side length The radius of gyration of the system about an axis perpendicular to the square and passing through centre is 1 2 2 l 2 3 l 4 2 The radius of gyration of a thin rod of length about an axis passing through its one end and perpendicular to it would be

A smooth block of mass 10 kg moves up from bottom to top of a wedge which is moving with an acceleration a 3 m s Find the work done by the pseudo force measured by the person sitting at the edge of the wedge how do w bo that it 3m h 4m 11 720 3m 3m m

When a disc rotates with uniform angular velocity which of the following is not true Rate of change a The sense of rotation remains same b The orientation of the axis of rotation remains same c The speed of rotation is non zero and remains same d The angular acceleration is non zero and remains same

Three identical particles each of mass m are kept at the vertices of an equilateral triangle of side If the system rotates with a constant angular speed oo the energy of rotation is equal to A B ml w C ml w 4 3ml w 4 0 D none of these m

38 A device Fig 1 26 consists of a smooth L shaped rod located in a horizontal plane and a sleeve A of mass m attached by a weight less spring to a point B The spring stiffness is equal to x The whole system rotates with a constant angular velocity o about a vertical axis passing through the point O Find the elongation of the spring How is the result affected by the rotation direction Fig 1 25 A O R Fig 1 26 A BI

33 A small mass attached to a string rotates on a frictionless table top as shown If the tension in the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2 the kinetic energy of the mass will AIPMT Mains 2011 1 Increase by a factor of 4 2 Decrease by a factor of 2 3 Remain constant 4 Increase by a factor of 2

A circular ring of diameter 40 cm and mass 1 kg is rotat ing about an axis normal to its plane and passing through the centre with a frequency of 10 rps Calculate the angular momentum about its axis of rotation 2 51 kg m2 s 11

3 A square plate of side 1 has mass M What is it moment of inertia about one of its diagonals M1 MI a b c 6 M1 3 d 12 MI 4

23 A cylinder is being pulled slowly with the help of a long uniform rope on a horizontal floor as shown in the figure The pulling force lying applied at the end A is so adjusted that the length BC of the rope touching the cylinder always subtends angle 0 sin 0 8 at the centre of the cylinder and the length of the hanging portion CD always remains half of the length DE being dragged on the floor Find coefficient of friction between the rope and the floor A B 0 ng Str C D Ano H coto 3 8 E

A uniform disc is rolling on a horizontal surface at a uniform speed of 3 rps The radius of the disc is 10 cm and its mass is 1 2 kg Calculate its i angular velocity ii linear velocity and iii kinetic energy of rotation 18 85 rad s 1 1 88 m s 1 1 066

The moment of a force of 25 N about a point is perpendicular distance of force Ans 10 cm 2 5 N m Find the from that point

48 The moment of inertia of a uniform semicircular disc of mass M and radius r about a line perpendicular to the plane of the disc through the centre is 2005 a Mr2 c Mr b Mr d Mr

Mass of an electron is 9 x 10 31 kg It revolves round the nucleus of an atom in a circular orbit of radius 4 0 with a speed of 6 x 106 m s 1 Calculate the linear kinetic energy and the angular momentum of the electron 1 62 x 10 17J 2 16 x 10 33 kg m s 1

A non uniform bar of weight W is suspended at rest by two strings of negligible weight as shown in Fig 1 68 The angles made by the strings with the vertical are 36 9 d 2m W 53 1 Fig 1 68 36 9 and 53 1 respectively The bar is 2 m long Calcu late the distance d of the centre of gravity of the bar from its left end NCERT 72 cm

8 A wire has resistance 12 ohm It is bent in the form of a circle The effective resistance betwee the two points on any diameter of the circle is 1 12 Q 3 3 Q 2 24 9 4 6 Q

8 Two rods each of mass m and length are joined at the centre to form a cross The moment of inertia of this cross about an axis passing through the common centre of the rods and perpendicular to the plane formed by them is me me me me 1 2 3 4 12 6 3 2 9 A solid sphere of mass M and radius R cannot have

A uniform thin circular ring of mass m m 0 4 kg and radius r has a small particle of the same mass m fixed on it as shown in the figure The line joining the particle to centre is initially horizontal The ground is frictionless Find the contact force magnitude exerted by the ground on the ring when the system is released from rest R O m 0 4 kg

A uniform disc of mass m and radius R is thrown on horizontal lawn in such a way that it initially slides with speed Vo without rolling The distance travelled by the disc till it starts pure rolling is Coefficient friction between the contact is 0 5 2 3 4 9g 5v 9g 3g 3v

A uniform rod of mass m and length starts rotating with constant angular acceleration a de constant couple in a horizontal plane about a fixed vertical axis passing through one end The hor component of the net force exerted on the rod by the axis when it has rotated by an angle r 2 B ma I R C mna 2 D none of these of thin ning of mass M and radius r is released from rest in the position shown F A ma thelf 2

In a merry go round a boy of mass 20 kg is revolving along a circular path of radius 10 m with an angular velocity of 6 rpm What is the angular momentum of the boy 1 256 x 103 kg m s 1

A large platform is moving with constant acceleration a perpendicular to its plane in gravity free space A particle of mass m is projected with speed u relative to the platform at an angle 0 with the plane of the platform from a point O on it The angular momentum of the particle about O on the plate measured in the clockwise direction A always increases C remains constant B always decreases D first increases and then decreases

Figure shows a thin rod mass M length L suspended in a vertical plane by tying ideal strings at ends A and B Initially rod makes an angle 30 with horizontal and is at rest Now the string connected to the end B is cut Let T be the tension in the string connected to A and a be the magnitude of acceleration of point A just after the cutting event Pick correct option s A T 3mg 13 C T 4mg 13 B a A D a 3g 13 3 3g 13 A 0 30 LIE B

A flat disc of radius R lies on the horizontal surface The pressure between the disc and the surface decreases linearly with distance from the centre r due to its weight per unit area from 2Po at the centre to Po at r R at the circumference The coefficient of friction between the disc and the surface is u Find the power delivered by the external agent to rotate the disc with a constant angular velocity 5 A PR 6 3 B 7 PR 6 11 mp3 A 108 the pe

Consider a thin uniform square sheet made of a rigid material If its side is a mass m and moment of inertia I about one of its diagonals then 1 I 2 ma 24 3 I ma 12 I ma 2 12 2 ma 12