Rotation Questions and Answers

If we want to prove that body is in static equilibrium we will make Fx 0 Fy 0 Fz 0 for translational equilibrium but to prove rotational equilibrium about which pt we need to prove torque x torque y torque z 0

A small spherical insulator of mass 5 56 x 10 2 kg and charge 0 600 C is hung by a thin wire of negligible mass A charge of 0 900 C is held 0 150 m away from the sphere and directly to the right of it so the wire makes an angle 0 with the vertical see the drawing Find a the angle 8 and b the tension in the wire

7mR 2mR D A uniform rod AB of mass m length 2a is allowed to fall under gravity with AB in horizontal position When the speed of rod is v suddenly the end A is fixed The angular velocity of rod with which it begins to rotate will be 1 3 3v 2a 3v 2 4 5v 3a 5v

1 In the situation shown in the figure all the identical cylinders move such that there is no slipping anywhere The ratio of angular speeds of upper cylinders to that of lower cylinders is 3V 38 1 3 4 2 7 4 3 4 7 4 4 3 4V

4 333 3 W 10 ABCD represents a uniform square lamina as shown in the figure The moment of inertia along the corresponding axis are also indicated The ratio 2has a value 4 4 L h 1 1 4 2 4 3 3 1 1 4 2 1 1 2

21 The radius of gyration of a uniform circular disc o radius 28 cm about an axis passing through centre of mass and perpendicular to its plane is approximately 1 18 cm 3 28 2 2 14 2 cm 4 14 cm

The block below has 2 applied loads as shown The force F is 10 0 25 lb The force G is 29 10 0 lb What is the moment that these 2 loads create about the z axis going through point C in lb ft Z G Y A X 3 ft B C F 3ft 2ft

cyclic process is as shown on volume temperature V T diagram then on pressure volume P V diagram it will be shown as 1 3 PA P V 2 4 T PA 7 V

6 A solid sphere of mass m and radius r is placed o top of the incline and it undergoes pure rolling the its speed at the bottom of the incline equals to 1 10gh 7 2 fixed gh

A particle moves under the influence of central force field f r 7 where r 7 7 being the position vector of the particle relative to the centre of force O Show that the angular momentum of the particle about O is constant

A particle A moves along a circle of radius R 50 cm so that its radius vector r relative to the point O figure rotates with the constant angular velocity 0 40 rad s Then modulus of the velocity of the particle and the modulus of its total acceleration will be R A v 0 4 m s a 0 4 m s v 0 32 m s a 0 32 m s B C v 0 32 m s a 0 4 m s Dv 0 4 m s a 0 32 m s

A block is placed inside a horizontal hollow cylinder The cylinder is rotating with constant angular speed one revolution per second about its axis The angular position of the block at which it begins to slide is 30 below the horizontal level passing through the center Find the radius of the cylinder if the coefficient of friction is 0 6 What should be the minimum constant angular speed of the cylinder so tha the block reaches the highest point of the cylinder REE 2001

24 20 2 A thread is wound on two identical bobbins placed on a horizontal flo with their axes parallel Radius of the outer flanges of the bobbins is times of that of the inner spools The midpoint of the thread is pull vertically upwards with a constant velocity u If the bobbins roll on t floor without slipping find velocity of approach of their centres wh angle between thread segments becomes 20

Block of mass m is released from height R inside a smooth hollow sphere of same mass m and radius R Friction on ground is sufficient to prevent slipping of hollow sphere The kgR speed of hollow sphere is 10 when block reaches lowest point of sphere Find the value of k 3 R R m R 9 Hollow sphe

35 If an axis is passing through the centre of a sphere then radius of gyration about a parallel axis at a distance 2 R from first axis is M Mass of sphere R Radius of sphere 1 5 R 3 5 2 R 4 22 5 IS 10 5 R 20 R

solid circular disc m R is rolling without slipping upon a rough horizontal surface with angular speed The angular momentum about point O is 5 1 mR 4 3 2 2 mR2 mR 3 MR2 1 mR 2 H O xm m R 2R R

slipping by a string wrapped around it If the string is pulled with velocity v then centre of the cylinder moves with velocity v equal to 1 v 2 2v N 3 4 Zero dari fand warfa for I af at van Vo C fer V C

A circular ring having mass M 4 m and radius R is attached to a small smooth ring of mass m kept at point A The ring is threaded onto a horizontal fixed frictionless wire B A Initially the bigger ring is held horizontally alongside the wire in such a manner that initially the planes of both the rings are at 90 to each other and the planes of smaller and bigger rings are perpendicular to the plane of the paper x y plane Now the bigger ring is released from rest After release the planes of smaller and bigger ranges remain perpendicular to the plane of paper x y plane 100 the angular speed of bigger ring at the instant it is vertical is g B 23R 5 g 6 V3R y C 10 g 85R X D g 3R

A ring of radius r is moving without slipping on a circular track of radius R Angular speed of the ring about its axis is Ignoring the fact that the ring axis is inclined A the angular acceleration of the ring is 4 B the angular acceleration of the ring is co r R R r R C the angular velocity of centre of the ring about vertical axis passing through the centre of track is ro R D the angular velocity of centre of the ring about vertical axis passing through the centre of track is R r

From the top of a tower a particle is thrown vertically downwards with a velocity of 10 m s The ratio of the distances covered by it in the 3rd and 2nd seconds of the motion is Take g 10 m s 1 O 5 7 2 3 4 O 7 5 3 6 6 3

A uniform rod of mass m and length L is placed on the fixed cylindrical surface of radius R at an small angular position from the vertical vertical means line joining centre and vertex of the cylindrical path as shown in the figure and released from rest Find the angular velocity of the rod at the instant when it crosses the horizontal position Assume that when rod comes at horizontal position its mid point and vertex of the circular surface coincide Friction is sufficient to prevent any slipping L 2 R L 2

1 A non uniform disk rolls without slipping on a rough ground The mass of the disk is 5 kg moment of kgm radius is 3m At the instant shown the centre of mass lies on a horizontal 175 inertia about O is diameter at a distance I m from 0 The angular velocity at this moment is rad s What is the force of 5 friction in N at this moment 0 cm 1m

Q 27 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 Option 1 181 2 MR option 2 19 MR 2 Option 3 55 MR 2 Option 4 73 MR 2 9

A point mass m is welded to a uniform ring of mass m and radius R as shown in the figure m Assume that the ring does not slip and initially the system is released with very small angular velocity What will be the speed of the point mass as seen from the ground after the ring ha turned through an angle of 90 Assume ring does not fall side ways O gR O gR 2

Two circular discs of same weight and thickness are made from metals of different densities Which disc will have the larger moment of inertia about its central axis Disc with larger density Disc with smaller density Both will have same moment of inertia More information is required

Two identical ladders are arranged as shown in the figure Mass of the block is m and the mass of each ladder is M The length of each of the ladder is L The system is in equilibrium What is the magnitude of frictional force acting at A or B B C A Xe mg Cos cos M m gcos 0

A body is projected vertically upwards from ground If t and t be the times at which it is at height h above the projection while asoding and descending respectively then his 1 2

Figure shows a composite pulley of that consist of two cylinders of R and 2R stacked MR coaxially Moment of inertia of composite pulley is A light string is wound over pulley and another pulley A of mass M is hanged through the string as shown in figure SRAMAY 2 3R C Go down with velocity Ro M MR2 The composite pulley is rotated with angular velocity o in the direction shown The pulley A will A Go up with velocity AYATHE B Go up with velocity Ro D Will not move

A solid cylinder of radius R is projected with velocity vo on a rough horizontal surface of coefficient of friction u at t 0 and at the same instant it has an angular 4v0 velocity of R as shown in figure Then 3 The cylinder stops at 1 and then turns back Vo g the cylinder starts pure rolling Att Atl Att 5vo 3 g Vo angular velocity of the cylinder is g 3vo ng speed of the cylinder is vo 2V0 R 4v R

24 A wheel rotating at same angular speed undergoes constant angular retardation After revolution angular velocity reduces to half its initial value It will make revolution before stopping

A solid cylinder of mass 2 kg and radius 4 cm rotating about its axis at the rate of 3 rpm Th torque required to stop after 2 revolutions is 1 2 x 10 6 Nm 2 2 x 10 3 N m 3 12 x 10 4 Nm 4 2 x 106 N m

D 4 cm sec Q 2 The angular velocity of a fan is dependent on time t as shown in figure How many revolutions the fan will produce in 5 minutes 500 01 2 345 Time min A 500 revolution B 1000 revolution C 2000 revolution D 4000 revolution 164 Q 2 Rager Prote 15 P 0 wxt 0 1x1x500 44x500 1 XIXSOO 2 500 2000 Q1 23580 27 Q3 A system of three masses is shown in int air positions What Angular speed rev min 500 A 500 B 1000 C 2000 D 4000 012345 Time min 2ant 2s 500 3x 590 C R 7 Q 3 i 4 n 220

4 In the diagram shown the weight of the rod is W and it is a uniform rod A small weight W 2 has been placed at a distance 3L 4 from the wall The force applied by the rod on the wall is only in the horizontal direction What is the value of X a 7L 4 b 5L 12 X String c L 3 Block d None

ring of mass M and radius R is tied with string at one end and is free to rotate about hinge on other end Find Tension IT a se Solution Steps to be followed Draw forces Mg will act centre of mass you know COM of semi ring is at from centre 2R I net 0 about hinge Mg x 2R T Mg TV T 2R 0 COM 2R TC 2R IMG T Hinge reaction

7 The figure shown is an overhead view of a thin uniform rod of length L and mass M rotating horizontally at angular speed about an axis passing through its centre A particle of mass m initially attached to the endA is ejected from the rod with velocity V which is perpendicular to the rod at the instant of ejection If 10 0 rad s L 1 0 m m M and and V is 4 m s more than the speed of rod end A just after the ejection then the value of Vis 1 4 m s 3 6 m s 2 5 m s 4 7 m s add your responses Type Text A Asked by 2006987 aesl id Standard XI Stream JEE Aug 1 2021 at 1 02 PM Type your answer here OR YOU can upload an

The light circular hoop of radius r carries a heavy uniform band of mass m around half the circumference and is released from rest on the incline in the upper position shown At a particular instant the hoop has rolled without slipping one half of a revolution A Moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of the hoop is mr B Change in potential energy of the hoop is mgr cose sin C Angular velocity of the hoop is 4 cos 0 sin 0 R 2 D The angular acceleration of the hoop is 10 g sin 0

A cubic frame is made of 12 rods each of mass m and length l A B 1 2 3 D 4 L E H 0 Question Type Multiple Correct Type I C of cube AB is 3 K J F The moment of inertia of the cube about its face 23 me diagonal BD is 3 The moment of inertia of the cube about an axis passing through the center of cube and perpendicular to one of 14 the face HI is 3 3 me The moment of inertia of the cube about one of the side 32 me The moment of inertia of the cube about an axis passing through the center of the face and the midpoint of the one of 23

The angular velocity of a body changes from 6 rad sec to 54 rad sec without applying torque but by changing moment of inertia The ratio of the initial radius of gyration to the final radius of gyration is 1 2 1 3 5 13 A cylinder is wranno 2 1 9 4 3

A rigid uniform horizontal wire PQ of mass M pivoted at P carries a constant current It is made to rotates with a constant angular speed on a horizontal circular conducting smooth frame in a uniform vertical magnetic field B If the current is switched off then the angular acceleration of the Find BI wire in terms of B Mand is given by n M the value of n

31 A cylinder is released from rest from the top of an incline of inclination 0 and length I If the cylinder rolls without slipping then what will be its speed when it reaches the bottom a C 3 6 V7 gl sin 0 gl sin 0 b 3 gl sin 0 d None of these

x Three uniform rods each of mass M and length L are placed along the three axes of a cartesian co ordinate system with one end of each rod at the origin The moment of inertia of the system about Z axis is a c ML 3 ML2 b 2ML2 3 d 2ML

A large slab of mass 5 kg lies on a smooth horizontal surface with a block of mass 4 kg lying on the top of it The coefficient of friction between the block and the slab is 0 25 If the 4 kg block is pulled horizontally by a force F 6 N the work done by the force of friction on the slab between the instants t 2 s and t 3 s is g 10 ms a 2 4 J b 5 55 J c 4 44 J d 10 J 4 kg 5 kg F

5 42 A spool has a mass of 2 kg an inner radius R 3 cm and an outer radius R 5 cm the radius of gyration about the axis of the spool is K 4 cm A constant horizontal force of 5 N is applied to the free end of a massless thread that is wrapped around the inner cylinder of the spool as shown in figure 5 150 If the spool rolls without slipping calculate the linear acceleration along the horizontal surface What is the minimum coefficient of static friction required to prevent slipping R 7777 Ans a 2 439 m s M Figure 5 150 min 0 0062 F 5 Nt

Example 9 22 A solid flywheel of 20 kg mass and 120 mm radius revolves at 600 revmin With what force must a brake lining be pressed against it for the flywheel to stop in 3s if the coefficient of friction is 0 1

Q 3 Option 710 0 Moment of inertia of an equilateral triangular lamina ABC about the axis passing through its centre O and perpendicular to its plane is I as shown in the figure A cavity DEF is cut out from the lamina where D E F are the mid points of the sides Moment of inertia of the remaining part of lamina about the same axis is 16 1 Option 2 15 Io Option 3 310 4 Option 4 31 lo 32 A Correct Answer D E B

A horizontally uniform rod AB of mass m and length 1 rotates freely about a stationary vertical axis 00 passing through the end A which is located exactly midway between O and O and OO 1 At what angular velocity in units of the rod is the horizontal component of the force acting on the lower end of the axis OO equal to zero g 10 m s 1 5m l 3m pip lo B

A particle of charge q and mass m is clamped rigidly at the circumference of a ring with mass m and radius R Initially ring is in vertical plane resting on a sufficiently rough horizontal surface with charge q at the same horizontal level as that of the centre of the ring There exists uniform horizontal electric fields as shown 22 At t 0 the system is let free Given that qE mg 7 The magnitude of the friction force at t 0 is mg A mg B 2 mg Co 2 Work done by the electric field when the ring has rotated through 90 is 4 A mgR B 7mgR C mgR Speed of the centre of mass of the system after 90 rotation is W Rg 11 28 2 B Rg 28 C 4 Rg 28 D m R D mg 2R 9 m Sufficiently rough to avoid slipping D Rg E

O B 6 A light ring of radius r wearing two identical beads A and B each of mass m is hinged at its top point O in such a way that it can rotate freely in its plane about a horizontal axis through the hinge O The bead A is affixed on the ring and the bead B is held so that they occupy positions of the ends of the horizontal diameter of the ring and the system stays motionless The ring is well lubricated so that the bead B can slide with negligible friction on the ring Determine acceleration of the beads immediately after the bead B is released and final angle of rotation of the ring when all motion ceases after a long time due to the little viscous friction between the bead B and the ring Acceleration due to gravity is g

A man stands in contact against the inner wall of a hollow cylindrical drum of radius R rotating about its vertical axis with some angular speed If the coefficient of friction between the wall and his clothing is 0 5 and floor is suddenly removed then the possible rotational speed of the cylinder to enable the man to remain stuck to the wall without falling is Lok Lola

82 y intercept 16 897 cm 4 853 Calculation of equivalent force couple at A means the calculation of R and M Solution Ans Example 4 6 A bracket is subjected to a coplanar force system as shown in Fig 4 9 Determine the magnitude and line of action of single resultant of the system If the resultant is to pass through b what should be the magnitude and direction of a couple 250 N 450 N EMA F FE 1m 100 N m R EF EF 150 B 60 1m Figure 4 9 Example 4 6 250 N