Rotation Questions and Answers

Consider a solid rod of mass m and uniform density resting against a vertical wall and horizonta floor as shown in the figure The coefficients of friction of the rod with the wall and with th floor are given to be and respectively Gravity is acting downwards with acceleration due t gravity g What should be the value of the inclination angle a so that the rod stays in equilibrium X1 tan 1 X 2 tan 3 tan 1 th H F 1 2 2 1 2 11 1 1 1 2 2442 m H F G

26 Moment of inertia of a uniform thin rod of mass and length L about the perpendicular bisector xy I Now the rod is bent about the midpoint on the plane normal to the axis xy to form an L Momen of inertia of the system about axis xy will be 1 1 2

A small ring P is threaded on a smooth wire bent in the form of a circle of radius a and center O The wire is rotating with constant angular speed w about a vertical diameter XY while the ring remains at rest relative to the wire at a distance a 2 from XY Then w is equal to

A spool consider it as a double disc system joined by a short tube at their centre is placed on a horizontal surface as shown in figure A light string wound several times over the short connecting tube leaves it tangentially and passes over a light pulley A weight of mass m is attached to the end of the string The radius of the connecting tube r and mass of the spool is M and radius is R Find the acceleration of the falling mass m Neglect the mass of he connecting tube and slipping of the spool N M

A homogenous cylinder of mass m and radius ris pulled on a horizontal plane by a horizontal force F acting on its centre of mass Assume rolling without slipping The acceleration of the centre of mass of the cylinder will be F 2m 2F 3m FIE m 3F 2m

A solid cylinder of mass M and radius R rotates about an axis passing through its centre making 60 rpm Its kinetic energy of rotation is 4 MR 2 MR MR 6 MR

hr mi The radius of gyration of a hollow sphere of mass m and radius R about an axis which is at a distance 2R from surface and parallel to its diameter will be

A rod of mass M and length I is placed in a horizontal plane with one end hinged about the Mg is vertical axis A horizontal force of F 2 5L applied at a distance from the hinged end The angular acceleration of the rod will be 6

3 mL 25 Three uniform rods each of mass m and length L metre are connected to form an equilateral triangle Calculate the M O L of the system about an axis passing through one of the vertex and L to the plane of the triangle m L m L L m C Ans mL M O I of the rod AB and AC about the given axis are each equal tomL an axis passing through square Ans M 4 SL M O I about AB Mr Ma M 2M 29 In the above questi Ans M 5 8 5

A rope is wound around a hollow cylinder of mass 5 kg and radius 20 cm If rope is pulled with a force of 20 N the angular acceleration of the cylinder will be 20 rad s 30 rad s 40 rad s 10 rad s

cally on a set of three hemispheres placed in contact with each other on smooth horizontal ground from a height h Mass of each hemisphere is 2 and radius of each body is R LJ TOP VIEW SIDE VIEW Neglect any rebounding of hemisphere If sphere comes to rest after the simultaneous collision with three hemispheres then ration of KE of sphere before collision and KE of any hemisphere after collision is p then find the value of p I

A top spins at 30 rev s about an axis that makes an angle of 30 with the vertical The mass of the top is 0 50 kg its rotational inertia about its central axis is 5 0 x 10 4kg m and its center of mass is 4 0 cm from the pivot points If the spin is clockwise from an overhead view what is the precession rate 9

A thin uniform straight rod of mass 2 kg and length 1 m is free to rotate about its upper end When at rest it receives an impulsive blow of 10 Ns at its lowest point normal to its length as shown in figure The kinetic energy of rod just after impact is T 10 NS

A uniform rod of length and mass m is rotating about a fixed axis perpendicular to the paper xy plane and passing through its one of the end A At the instant shown in the Figure rod s angular velocity is and velocity of the centre of mass of the rod is Vcm The moment of inertia of the rod about an axis passing through its centre of mass and parallel to k is ICM and the moment of inertia of the rod about an axis passing through point A and parallel to k is IA LA and k represent the angular momentum of the rod about point A and kinetic energy of rod respectively A cm cm M

4 A rigid body is made of three identical thin rods each of length L fastened together in the form of letter H The body is free to rotate about a horizontal axis that runs along the length of one of the legs of the H The body is allowed to fall from rest from a position in which the plane of H is horizontal What is the angular speed of the body when the plane of H is vertical g 1 S 3 g 1g 2 2 2VL 4 2 g B

A uniform solid cylinder of mass 10 kg can rotate about a frictionless axle through its center O as shown in the cross sectional view in the figure A rope wrapped around the outer radius R 1 0 m exerts a force of magnitude F1 5 0 N to the right A second rope wrapped around another section of radius R2 0 50 m exerts a force of magnitude F2 6 0 N downward How many radians does the cylinder rotate through in the first 5 0 seconds if it starts from rest F F R R

A cinder block of mass m 4 0 kg is hung from a nylon string that is wrapped around a frictionless pulley having the shape of a cylindrical shell as shown in the figure If the cinder block accelerates downward at 4 90 m s2 when it is released what is the mass M of the pulley M E

A simple pendulum of length 40 cm oscillates with an angular amplitude of 0 04 rad Find a The time period b The linear amplitude of the bob c The speed of the bob when the string makes 0 02 rad with the vertical d The angular acceleration when the bob is in momentary rest take g 10 m s

1 meter 2 1 1kg m s 2 10kg m s 3 40kg m s 1 no idea 41 In which case the angular acceleration will more with respect to rotational axis T Grill Case I X T Case II F 1 Case I 2 Case II 3 Same 4 None If two mass particles of masses 2 kg and 4 kg are attached to two ends of string of length 10 m are set in rotational motion in a horizontal plane about the axis which is at distance 4 m from mass particle as shown in figure with constant angular velocity o Find Ratio of tension T T at both the ends

tions 31 Arm 4 0 kg Hand 1 0 kg 0 10 m 0 60 m Note Figure not drawn to scale In order to model the motion of an extinct ape scientists measure its hand and arm bones From shoulder to wrist the arm bones are 0 60 m long and their mass is 4 0 kg From wrist to the tip of the fingers the hand bones are 0 10 m long and their mass is 1 0 kg In the model above each bone is assumed to have a uniform density 31 When the arm and hand hang straight down the distance from the shoulder to H Arm Hand 1 0 kg 0 10 m 4 0 kg 0 60 m Note Figure not drawn to scale 32 The arm is held in the horizontal position and the hand is bent at the wrist so the fingers point up as shown in the figure above The torque exerted by the weight of the hand with respect to the shoulder is most nearly the sho A 6 N m B 10 N m C 30 N m D 60 N m E 70 N m 4260

9 A block of mass 250 g slides down an incline of inclination 37 with a uniform speed Find the work done against the friction as the block slides through 10 m m is kent over another block of mass

A uniform rod of mass m and length is hinged at upper end Rod is free to rotate in vertical plane A ball of mass m moving horizontally with velocity v collides at lower end of rod perpendicular to it and sticks to it The minimum velocity of the ball such that combined system just completes the vertical circle will be 1 2 2gf 3 2 gl 2 2gl gl

A disc of mass m and radius R is rolling without slipping on a horizontal floor such that velocity of its centre of mass is v Its angular momentum about instantaneous axis of rotation is A 1 mvR mvR 2 4 3mvR 2 5mvR

1 A heavy ring of mass m is clamped on the periphery c a light circular disc A small particle having equal mas is clamped at the centre of the disc The system i rotated in such a way that the centre moves in a circle of radius r with a uniform speed v We conclude that an external force must be acting on the central particle a b c d mu 2 r 2mv r 2mv 2 2 r 2mv r 2 must be acting on the central particle must be acting on the system must be acting on the ring

Two masses of 200 g and 300 g are attached to the 20 cm and 70 cm marks of a light metre rod respectively The moment of inertia of the system about an axis passing through 50 cm mark is D 0 15 kg m 0 03 kg m 0 3 kg m Zero Solution Repo

A uniform wheel of moment of inertia I as shown is pivoted on a horizontal axis through its centre so that its plane is vertical A small mass m is stuck on the rim of the wheel as shown The angular acceleration of the wheel when mass is at point A is a and when mass is at point B is CLB Then B mgr Coso a sin 0 1 a sine 3 A as cose 2 x mor 4 ak a A thin uniform red of mass m moves translationally with acceleration CLA an cos 0 A due to

R Mech 3 A student holds one end of a thread which is wrapped around a cylindrical spool as shown above The student then drops the spool from a heighth above the floor and the thread unwinds as it falls The spool has a mass M and a radius R and the thread has negligible mass The spool can be approximated as a solid cylinder of moment of inertia 1 MR Express your answers in terms of M R h and fundamental constants a Calculate the linear acceleration of the spool as it falls Thread de 10 HAKK b Calculate the angular velocity of the spool just before it strikes the floor At time 1 0 the spinning spool lands on the floor without bouncing and comes free from the thread It continues to spin but slips on the floor s surface while doing so Assume a constant coefficient of sliding friction c Calculate the angular velocity of the spool as a function of time 1 d Calculate the horizontal speed of the spool as a function of time assuming the horizontal speed is zero at time 0 e At what time does slipping between the spool and floor cease

A jewel smith wishing to buff a finished piece of jewelry attaches a buffing disk to his drill The radius of the disk is 2 80 mm and he operates it at 2 20 x 10 rad s a Determine the tangential speed in m s of the rim of the disk m s b The jeweler increases the operating speed so that the tangential speed of the rim of the disk is now 285 m s What is the period of rotation in seconds of the disk now S

EX 1 A uniform rod of length 4 m weighs 50 N 1m of the rod lies on a horizontal table and the rest lies over the edge Where does the reaction act when the rod is about to tilt b What downward force must be applied to the end of the rod to stop it from tilting What is the reaction of the table on the rnd when it is about to tilt

5 A particle is kept fixed on a turntable rotating uniformly As seen from the ground the particle goes in a circle its speed is 20 cm s and acceleration is 20 cm s The particle is now shifted to a new position to make the radius half of the original value The new values of the speed and acceleration will be 2 a 10 cm s 10 cm s c 40 cm s 10 cm 2 b 10 cm s 80 cm s 2

A plastic circular disc of radius R is placed on a thin oil film spread over a flat horizontal surface The torque required to spin the disc about its central vertical axis with a constant angular velocity is proportional to nswer A B Your Attempt R R Correct answer Rate this ques

136 A tangential force Facts at the top of at spherical shell of mass m and radius R 1 acceleration of the shell if it rolls with slipping is 1 3 5F 3m R 2 4 15 95 6F 5m 2F 3m

A uniform 255 N rod that is 2 10 m long carries a 225 N weight at its right end and an unknown weight W toward the left end Figure 1 When W is placed 55 0 cm from the left end of the rod the system just balances horizontally when the fulcrum is located 75 0 cm from the right end Find W Express your answer with the appropriate units W 115 N Subnyl Previous Answers Correct Correct answer is shown Your answer 115 3 N was either rounded differently or used a different number of significant f Important If you use this answer in later parts use the full unrounded value in your calculations Part B If W is now moved 25 0 cm to the right how far must the fulcrum be moved to restore balance Express your answer with the appropriate units PA

inertia about a line perpendicular to the plane of the wire passing through the centre is ML T 1 ML 2 2 ML 5 T 1 ML T Question Type MCQ Question ID 8643515

4 3 A cubical block of side L rests on a rough horizontal surface with coefficient of friction u A horizontal force F is applied on the block as shown If the coefficient of friction is sufficiently high so that the block does not slide before toppling the minimum force required to topple the block is F A Infinitesimal B mg 4 C mg 2 D mg 1 77 A Figure 4 103 L

R 39 st 39 A homogeneous sphere of radius R 10 cm rotating about its vertical diameter is gently released on a hole of radius r 8 0 cm made in a fixed horizontal slab Centre of the hole is vertically below the centre of the sphere The sphere stops in a time interval At 9 0 s Calculate time interval required to stop the same sphere if it is placed rotating with the same angular velocity on a hole of radius r 6 0 cm made in another identical horizontal slab A At At X R x 3 2

Two thin circular discs of mass m and 4m having radii of a and 2a respectively are rigidly fixed by a massless rigid rod of length 1 24a through their centres This assembly is laid on a firm and flat surface and set rolling without slipping on the surface so that the angular speed about the axis of the rod is The angular momentum of the entire assembly about the point O is L see the figure Which of the following statement s is are true coso l 2 W The magnitude of the 2 component of I is 55m 4m

Two objects a ring and a spherical shell of same mass and radius are released from the top of two identical inclined planes If they are rolling without slipping then ratio of speed of centre of mass of the two objects when they will reach the bottom of the inclined plane is O 5 3 O 5 6 O 5 2 O 5 1

A B 18 A uniform beam of weight W is attached to a wall by a pivot at one end and is held horizontal by a cable attached to the other end of the beam and to the wall as shown above T in the cable which makes an beam Which of the following with the a tension to p C W 2 cos 8 W 2 sin 8 W Cos W sin 8 T D E W W 0 van House 12100 Obtain

A uniform rod of mass 1 kg and length L 1 m stands vertical Rod is free to rotate about hinge at B in x y plane only A force F 31 41 5k starts acting on the rod at point A Then immediately after force F starts acting on the rod A angular acceleration of rod will be 9 k rad s B angular acceleration of rod will be 12 34 k rad s C reaction torque of hinge on rod about B will be 0 D reaction torque of hinge on rod about B will be 1 5Nm B A i

A solid disc of radius 5 cm rolls without slipping on a horizontal floor as shown with an angular velocity of 3 rad s and angular acceleration of 2 rad 2 The magnitude of acceleration of point P on the disc at the given instant is in cm s 30

Paragraph for Questions 11 and 12 The element of a spacecraft with axial mass symmetry and a reaction wheel control system are shown in the figure When the motor exerts a torque on the reaction wheel an equal and opposite torque is exerted on the spacecraft thereby changing its angular momentum in the z direction If all system elements start from rest and the motor exerts a constant torque M for a time period t the moment of inertia about the z axis of the entire spacecraft including the wheel is I and that of the wheel with the z axis of symmetry of the spacecraft alone is I The spin axis of the wheel is coincident Find the final angular velocity of spacecraft GITAL CLA Mt A 1 1 Reaction wheel Mt B I L M Motor Mt C 1 1 D Mt

A light string is wrapped on a cylindrical shell and a fraction of length of string is unwrapped A particle of mass 2M is attached on another end of string as shown The system is kept in a vertical plane and cylinder can freely rotate about the axis of cylinder Particle is released as shown in figur Assuming there is no slipping between cylinder and string Choose the correct options 2M A B C M 2R The angular velocity of cylinder just after string taut is The angular velocity of cylinder just after string taut is 8 Velocity of particle just after string taut is gR 16 D Velocity of particle just after string taut is 3 GR w 0 93 R DR

3 A circular disc of mass 2 kg and radius 1 3 ft is suspended from its rim Calculate the length of the equivalent simple pendulum which will have same time period as the circular disc Ans 0 5 ft

CLA A rigid body of mass 0 5 kg at F 21 j k is acted on by the forces F 1 3 2k and F 21 3j k Then A Acceleration of body is given by 61 8j 6k B Vector perpendicular to 7 and F is 53 3k C Torque acting on the body due to forces about the origin is 9j 11k D Force required to make the body at equilibrium is 31 4 3k

Jestion No 33 View in English homogenous cylinder of mass m and radius ris pulled on a horizontal plane by a horizontal force Facting on its centre of mass Assume rolling without slipping The cceleration of the centre of mass of the cylinder will be n F

3 For the shared area shown in Fig Q3 20 points a Determine the moment of inertia of the shared area about the y axis by using a vertical differential element b Find the radius of gyration ky c Extra credit 10 points find the moment of inertia of the shared area about the x axis and radius of gyration kx h Fig Q3 X

A mass m moves in a circle on a smooth horizontal plane with velocity vo at a radius Ro The mass is attached to string which passes through a smooth hole in the plane as shown a mu Vo m AIPMT Cancelled 2015 b 2mu

A bracket is subjected to a coplanar force system as shown in Fig Determine the magnitude and line of action from A of the single resultant of the system If the resultant is to pass through the point B what should be the magnitude and direction of couple 400 N 500 N 500 mm 400 mm 50 N m 400 N

4 A smooth sphere of radius R is made to translate in straight line with a constant acceleration a A particl kept on the top of the sphere is released from there a zero velocity with respect to the sphere Find the speec of the particle with respect to the sphere as a function of the angle 0 it slides