Rotation Questions and Answers

c You can paddle your cycle maximum three times per second If the diameter of driver paddle wheel is 20 cm and follower gear wheel is 8 cm what is the maximum speed in rpm that you can achieve

A disc of mass M and radius R can rotate freely in a vertical plane about a horizontal axis at O distance from the centre of the disc as shown in the figure The disc is released from rest in the shown position Wher disc rotates by 37 then choose correct option s M R

A uniformly dense solid cylinder of mass m and radius R is released from rest on an inclined plane and starts performing pure rolling During its downward journey along the incline the cyline moves distance t the angle of inclination from horizontal is a and the coefficient of friction is given as u The acceleration due to gravity is g downwards Air resistance is not present 2 D The acceleration of centre of mass of cylinder is The final angular speed of cylinder is 13 2g sina 3 0 The minimum coefficient of friction required so that there is no slipping is tan a 3 The final angular speed of cylinder i 4 gl sina 3 R 2 gl sin a

A disc is pulled by a force F acting at a point above the centre of mass of the disc The direction of frictional force fr acting on disc pushed on a rough surface will be represented by 1 3 fr fr 0 F F 2 4 Information insufficient F fr is

A rod of length and mass m is hinged at A It is released from horizontal position from rest When it comes to position AB and makes and angle of 30 with vertical A Then the angular velocity in this position is given as N 3g 2l 1 2 Find N 30 B

A section of ring of mass m radius R is hinged at A and connected to string at B and ring stay at equilibrium A Tension in string is mg 2 3 3 3 B Tension in string is 2mg 2 3 3 3 C Reaction forces developed at A is D None of these mg 3 81 2 3 3 CHAFFELY 60 14

1 a Two smooth cylinder with diameters 250 mm and 400 mm respectively are kept in a groove with slanting surfaces making angle 60 and 30 respectively as shown in Fig 1 a Determine the reactions at contact points A B C 500 N 60 800 N 30 Fig 1 a

The free end of the open link chain of total length L and mass pper unit Tength is released from rest at x 0 Determine the force R on the fixed end and the tension T in the chain at lower end of the non moving part in terms of x

A rod of length t and mass m is hinged at A It is released from horizontal position from rest When it comes to position AB and makes and angle of 30 with vertical wwww A Then the angular velocity in this position is given as N 3g 2 1 2 Find N 30 B

A solid sphere of mass 1kg and radius 10 cm is rolling down an inclined plane as shown It s acceleration is 6 m s Its angular acceleration is 300 rad s 3 The minimum friction coefficient required for pure rolling is 14 Friction is acting downwards 37

The uniform rod of mass M and length L shown in the figure is released from rest As the rod falls down due to gravity does the force on the rod remain constant Does the torque on the rod remain constant Draw the FBD of the rod when it has swung down by an angle about the hinge Indicate the direction of the hinge force on the rod at this instant At which position does the hinge exert maximum force on the rod

A square plate of side a is hinged at A and connected with elastic spring at B and plate is in equilibrium Spring is at its natural length when 0 0 and spring constant of the spring is k mg 3 1 3 a A 60 B 30 C 45 D 15 000000 K 20 un B

A uniform disc is rolling on horizontal surface under the action of force F as shown Choose the correct statement s B F O Friction force will act towards right O Friction force will act towards left Angular momentum of disc is same about point A and B Angular momentum of disc is different about point A and B A

A sheet ABCD has mass M Sides AB and CD are parallel to each other and perpendicula to BC The perpendicular distance of mid point of AD from side BC is half of length of BC then moment of inertia of sheet about axis AD is A O D Options Me 3 1 2 Me 3 4 f Me2 12 4M2 3 B C

Two boys are holding a horizontal rod of length L and weight W through two ends If now one of the boys suddenly leaves the rod what is t instantaneous reaction force experienced by the other boy

A uniform 2 5 kg disk of radius 30 cm is rotating around its central axis at an angular speed of 72 rad s At time t 0 a man begins to slow it at a uniform rate until it stops at t 8 s a By time t 5 s how much work had the man done b For full 8 s at what average rate did the man do work

A sphere is projected obliquely up a perfectly rough plane a Find that the equation of the path of the point of contact of the sphere and plane if a is the inclination of the plane to the horizon and vois initial velocity at an angle 8 to the horizontal line in the plane and rolling is pure b Find the distance travelled by the contact point between the first two successive moments at which it touches the incline after projection

A disc of mass 10 kg and radius 1m is set into pure rolling on a rough horizontal surface as shown in the figure At a particular instant point P figure which is at a distance from the centre O is R 2 found to have a speed of 2 ms and acceleration of 10 ms 2 The angular velocity of the disc at this instant is o rad s and the acceleration of centre of mass is a m s F 21 R The value of o is P

onsider a uniform rod of mass m and length 21 with two particles of mass m each at its ends Let AB be a line perpendicular to the length of the rod and passing through its center nd the value of n if moment of inertia of the system about AB isml

hanged over a pulley of mass m Friction coefficient between pulley and string is u such that e 2 1kg m m A There cannot be any slipping between string and pulley howsoever small m is B If m 4 kg there cannot be any slipping between string and pulley howsoever large m 1kg is C If m 6 kg there will slipping between pulley and string if m 8 kg

A man of mass m marks a point on the circum ference of a disc where he stands at t 0 The disc is f reely moveable and has mass M He soon starts to walk along the circumference of the disc Find the net ang le rotated by the man when he again reaches the same p oint Main doubt While solving answer Why we take w final theta T as there is friction torque on d isc net torque is only zero on whole system s o there must be some a acceleration

A solid hemisphere m R has the moment of inertia about axis 1 Diameter of 3 mR 5 MR 3 5 M I of hemisphere about axis 3 will be 1 2 2mR 45 173 2 2 5 mR 173 320 2 3 mR 4 M J of hemisphere about axis 2 which is parallel to diameter but passing through centre of mass will 83 1 mR 320 2 2 2 2 MR MR 4 2 3m1 MR 2 9 10 MR mR 1 No

A uniform disc of inner radius R and outer radius 2R as shown in the figure rotate about its axis to angular velocity and then carefully placed on a rough horizontal surface coefficient of friction is Then answer the following questions 17 Time when it comes to rest is 45 Ro A 28 g 25 Ro 56 g C B D 45 Ro 14 g 25 Ro 14 g By R

A satellite of mass m is with an initial speed u from the surface of the earth After it reaches height R R radius of the earth m ejects a rocket of mass 10 so that subsequently the satellite moves in a circular orbit The kinetic energy of the rocket is G is the gravitational constant M is the mass of the earth 1 2 3 DI 20 5m u 3m 8 m 21 11 113 GM 200 R 119 GM 200 R 5GM V6R 2GM

The four masses ma mb mc ma 2 lie on the corners of a rectangle on a frictionless horizontal surface They are rigidly connected by rods of negligible weight Another mass m ma of velocity V in the positive x direction collides with ma and sticks to it What is the velocity of me in x y coordinates right after the collision Please show the full solution legibly Happy

Uniform rod mass m and length initially horizontal is set in motion such that COM of the rod gets velocity v vertically upward and angular velocity co such that 2nx x 2 where n is a number The whole situation is shown in the figure B Radius of curvature of the path of particle situated at end A when it is at highest point of its 0 path is Here a is an integer Find a 8a 2g

kg 6 A uniform circular disc of mass M F radius R 1 m is fixed to vertical axis AB with the help of a rod of length L as shown The disc rolls on a horizontal surface and is free to rotate about its centre If there is no slipping at the point of contact of disc and horizontal surface then kinetic energy of the disc will be given o 2 rad s L 1 m A 00 1 3 J B L Disc M R 2 6 J

6 A uniform circular disc of mass M 1 kg radius R 1 m is fixed to vertical axis AB with the help of a rod of length L as shown The disc rolls on a horizontal surface and is free to rotate about its centre If there is no slipping at the point of contact of disc and horizontal surface then kinetic energy of the disc will be given 2 rad s L 1 m A 1 3 J 7 B o L Disc M R 2 6 J 5

A hollow sphere ICOM MR of mass 0 925 kg and radius 0 241 m rolls without slipping at a speed of 9 64 m s toward an inclined plane which is tilted 18 0 degrees above horizontal The ball rolls up the incline plane again without slipping How far do the ball go up the plane L before it comes to a momentary stop Assume there is negligible loss due to any friction in this process Image size S M L Max

FS 290N 36 70 F4 370Ny Gil Find Fg F3 350N F b A force of 10 KN acts at appoint P 2 3 4 m and has its line of act passing through Q 10 3 4 m i Find force in the vector form 02 marks X it of thi farga chor A 1 10 21 n 2 monl

A 3 kg uniform rod rotates in a vertical plane about a smooth pivot at B A spring of constant k 300 N m and of unstretched length 100 mm is attached to the rod as shown Knowing that in the position shown the rod has an angular velocity of 4 rad s clockwise determine the angular velocity of the rod after it has rotated through g 10 m s a 90 b 180 A 450mm B 150mm wwwwwww 200mm D is vertically bel 7 2

158 A uniform rod of mass m and length is resting on a smooth horizontal surface A particle of mass m 2 travelling with a speed vo hits the rod normally and elastically Find final velocity of particle and the angulam velocity of the rod 1 4 Avo m 20 Top view Rod m l

A bar hinged to the foundation at A and supported by a strut CD is subjected to a horizontal 50KN load at B as shown in fig find the tensile fore S in the strut and the reaction R at A B 1 22 m 1 22 m 90 50 KN 1 83 m 1 83 m

Situation 4 15 pts Determine the reactions at contact at A and C and pin support at B in the figure shown if a 5 kg mass is at rest at C Also determine the minimum magnitude of P applied on mass B for which the system will be in equilibrium Note All contact surfaces have the same angle of friction of 14 036 degrees r 2 mm 3 8 mm 2 m

133 Two uniform spheres shown in figure rotate separately on parallel axis The upper sphere has angular speed wo and lower sphere is at rest Now the two spheres are moved together so that their surfaces touch After a short time the two spheres now in contact are rotating without slipping Find the final rate of rotation of upper sphere in rad s given moment of inertia of upper sphere I 4 kg m moment of inertia of lower sphere 1 2 kg m a 2 m b 1 m n 12 rad s R a R b

139 A homogeneous rod of mass 3 kg is pushed along smooth horizontal surface by a horizontal force F 40 N The angle 0 in degree for which rod has pure translation motion Then the value of 0 30 g 10m s vertical F 40 N 7 163 250

2 134 A ring of radius 4a is rigidly fixed in vertical position on a table A small disc of mass m and radius a is released as shown in the figure When the disc rolls down without slipping to the lowest point of the ring then its speed in m s will be take g 10 m s and a 0 4 m 4a

A mass m is connected by a light cord to a mass m as shown Cord passes over a pulley of radius R and moment of inertia I The acceleration of two masses is a Choose the correct option T m OT T O T T O T T QI th la m Pa T la 2R la Ja

cal Take g 10 m s Figure shows a ring of radius 2 m and a rod of length The rod is moving with velocity 4 m s perpendicular to its length Find the angular speed in rad s of point of intersection A w r t O at the instant when 0 30 A 4 30 O V time

A rod of mass m and length 2R is attached to a circular ring of m and radius R along its vertical diameter as shown Horizontal force Fis applied at top Friction is sufficient for pure rolling then friction force acting on the ring at the instant shown is Ring m R 8E F

View in English A uniform ring of radius ris kept vertically on a rough surface and is rotated in clockwise sense with angular speed wo and left on the surface as shown Which of the following graph indicates variation of angular velocity with time 0 00 L

A uniform circular disc of mass mand radius R is free to rotate about a horizontal axis passing through its rim at A and perpendicular to its plane The disc starts falling in the clockwise sense from rest from the position shown At the instant the disc has rotated by 2 A Its angular velocity is 2 3R Its angular acceleration is 2g 3R Horizontal component of the force by the axis 4mg on the disc is 3

One end of a uniform thin rod AB of massless m and length is hanging froma mass string The other end is held at an angle of 45 with horizontal Find the tension in the string immediately after the support Bis removed LLL Fo B string A

A block and a cylinder with BmR2 both of mass m lin on a plane inclined at an angle e touching each other as shown in figure There is sufficient friction between the cylinder and the plans so that it rolis without slipping But the bottom of the block is coated with grease so there is no friction between it and the plane However there is a coefficient of kinetic friction u 1 between the block s right face and the cylinder Assume that is small onough so that the block s bottom face romains in contact with the plane at all times 1 What is the acceleration of block 0 3 gaine gsine 1 3 Bg sine 1 3 gsine 1 3 m m 0

A uniform disc of mass Mand radius R is given velocity vo and 200 at t 0 angular velocity wo R on rough horizontal surface as shown It starts pure rolling with velocity v at t to then H 000 D

Three particles each of mass m can slide on fixed frictionless circular tracks in the same horizontal plane as shown Particle A moves with velocity vo and hits particle B elastically Assuming that B and C are initially at rest and lie along a radial line and the spring is initially relaxed before impact then 2 R A Vo B the velocity of B immediately after impact is vo the velocity of C when the stretch in the spring is maximum is 2vo 5 4v0 the velocity of B when the stretch in the spring is maximum is 5 the maximum stretch in the spring in the spring is m 5k Vo

Select the incorrect option 1 The total momentum of a system of particles is equal to the product of the total mass of the system and the velocity of its centre of mass 2 In pure rotation all parts of the body have the same angular velocity at any instant of time 3 For rotation about a fixed axis the direction of o angular velocity does not change with time if Ti axis 0 4 For rotation about a fixed axis magnitude of

Paragraph for below question A uniform rod of mass M and length 1 m hinged at A in the vertical plane is released from rest when it is in horizontal position At angular position 8 60 angular velocity of rod is w Then g 10 m s 18 Q Tangential acceleration of end B at angular position 8 60 is Only One Correct Answer A 2 3g B C D 3 3g 3 3g 30 O

A B A B Initially Take a bicycle rim and extend its axle on both sides Tie two strings at both ends A and B as shown in the figure Hold both the strings together in one hand such that the rim is vertical If you leave one string the rim will tilt Now keeping the rim in vertical position with both the strings in one hand put the wheel in fast rotation around the axle with the other hand Then leave one string say B from your hand and observe what happens What will happen if we leave string B After a The rim will stop rotating D The rim will rotate in a vertical plane and the plane of rotation will precesses about string A The rim will rotate in a horizontal plane None of the above

A cubic frame is made of 12 rods each of mass m and length A E H O I C K B F L 23 A The moment of inertia of the cube about its face diagonal BD ismt B The moment of inertia of the cube about an axis passing through the center of cube and 14 perpendicular to one of the face HI isme 32 C The moment of inertia of the cube about one of the side of cube AB ismt D The moment of inertia of the cube about an axis passing through the center of the face 23 m and the midpoint of the one of the side JK is