Rotation Questions and Answers

43 A particle slides on the surface of sphere starting from the topmost point Find th angle rotated by the radius through the partic when it leaves contact with the sphere 1 cos 3 tan G 4 3 2 cos 4 tan 1 2 3 2 3

A rough L shaped rod is located in a horizontal plane and a sleeve of mass m is inserted in the rod The rod is rotated with a constant angular velocity in the horizontal plane The lengths and 2 are shown in the figure The normal reaction and frictional force acting on the sleeve when it just staps slipping are u coefficient of static friction between the rod and the sleeve A N mw N m g 0 B f mw l D f N 3 4 la 2

In the figure shown a cubical block is held stationary against a rough wall by applying a force F Select the incorrect statement a Frictional forcef Mg b F N Nis normal reaction c F does not apply any torque about C M d N does not apply any torque about C M M 2a a a F

A person holds a uniform 0 1 kg metre stick horizontally between fore finger and thumb in such a way that the thumb is at the end of the meter stick and the finger is 30 mm from it The forces exerted by the thumb and fore finger act vertically as shown in the diagram below Calculate the force exerted by the thumb When performing the calculations please ensure you include all additional forces and distances to the diagram Ffore finger 30 mm Fthumb 1 m

If a tension in a string is 6 4 N A load at the lower end of a string is 0 1 kg the length of string is 6 m then find its angular velocity g 10 m s A 3 rad s C 2 rad s B D MH CET 2008 4 rad s 1 rad s

Variable F F2 F3 0 d d2 F Values for the figure are given in the following table Note the figure may not be to scale Value 200 N d d3 590 N 310 N 25 degrees 2m 3 m 4m 0 N m F2 Which direction is MR o rotating F3 a Using Varignon s Theorem determine the magnitude of the resultant moment MR o produced by the forces about point 0 Round your final answers to 3 significant digits figures MR O

A 500 0 g bird is flying horizontally at 2 50 m s not paying much attention when it suddenly flies into a stationary vertical bar hitting it 25 0 cm below the top Figure 1 The bar is uniform 0 800 m long has a mass of 2 50 kg kg and is hinged at its base The collision stuns the bird so that it just drops to the ground afterward but soon recovers to fly happily away Figure Bird 25 0 cm 1 of 1 Part A What is the angular velocity of the bar just after it is hit by the bird Express your answer in radians per second V AEO Submit Part B Constants Request Answer BAVE What is the angular velocity of the bar just as it reaches the ground Express your answer in radians per second rad s

Q 10 A rod of mass m hinged at one end is free to rotate in a horizontal plane A small bullet of mass m 4 travelling with speed u hits the rod and attaches to it at its centre Find the angular speed of rotation of rod just after the bullet hits the rod 3 take length of the rod as l 6 u 2 13 1 1 3 6 u 19 1 3 u 3 u

surface with a velocity of Vo It then ascends a smooth continuous track as shown in figure Find the velocity v if maximum height by which its centre will rise is 3 6 m g 9 8 m s 2 O Vo 3 9 m s 0 O 8 4 m s

A top consists of a uniform disk of mass m0 and radius ro rigidly attached to an axial rod of negligible mass A top is placed on a smooth table and set spinning about its axis of symmetry with angular speed ws a How much work must be done to set the top spinning b Evaluate your result form0 0 1kg r0 4cm andws 100 c The center of the disk is a distanced 2cmfrom the point of contactwith the table What is the precession frequencywp

9 Incorrect statement among the following is Total torque on a system is independent of the origin if the net external force is zero Direction of angular momentum is not necessarily along the angular velocity Vanishing of total external torque and total external force are independent conditions For a body to be in rotational equilibrium acceleration of centre of mass of the body should be ze

KOTA A disc of mass m is rolling without slipping on a rough surface The velocity of centre of mass of disc is 10 m s Find the velocity of point A which makes an angle 30 from horizontal as shown in figure A V 151 3 5 C V 151 5 3j B VA 151 5 31 D VA 151 5 3 130 OV

A rod of length 1 m is pivoted about horizontal axis with a frictionless pin The rod is released from rest in vertical position What will be velocity of centre of mass assume uniform mass distribution when rod is inclined at an angle of 60 from vertical g 10 ms 2 Rod 60 Pivot 1 3 75 ms 1 7 5 ms 1 4 25 ms 1 7 5 ms 1

3 A uniform cylinder of radius R is spinned about its axis to the angular velocity w and then placed into a corner Fig 1 58 The coefficient of friction between the corner walls and the cylinder is equal to k How many turns will the cylinder accomplish before it stops R Fig 1 58

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 s The coefficient of friction between the ground and the ring is large enough that rolling always occurs and the coefficient of friction between the stick and the ring is P 10 The value of P is round Stick

A uniform ring of radius r 1 metre and mass mis rolling without slipping with velocity v towards a step of height b 0 9 m on a horizontal surface Assume that ring does not rebound and no slipping occurs at point of contact when the ring rolls up If the minimum velocity needed for ring to roll up the step is m s find x g 10 m s 0 9 m

A solid sphere of mass m and radius R is kept on a rough surface the velocity of air density p around the sphere area is as shown in fig assuming R to be smal and m 4 R kg the minimum value of coefficient of friction so that sphere stars g pure rolling is Assuming force due to pressure difference is acting on the B center of mass of sphere find the value of m Tmls air R 14m s air

5 52 A constant net torque equal to 20 N m is exerted on a pivoted wheel for 8 sec during which time the angular velocity of the wheel increases from zero to 100 re min The external torque is then removed and the wheel is brought to rest by friction in its bearings in 70 sec Compute a the moment of inertia of the wheel about the rotation axis b the friction torque c the total no of revolutions made by the wheel in the 70 sec time interval Ans 15 3 kg m 2 29 N m 58 3 revl

1 In the diagram on the right a plank weighing 120N is supported by two trestles at points A and B A man weighing 480 N is standing on the plank a Redraw the diagram showing all the forces acting on the plank b Calculate the total clockwise moment of the two weights about A c Use the principle of moments to calculate the upward force from the trestle at B d What is the total downward force on the trestles e What is the upward force from the trestle at A f The man now walks past A towards the left hand end of the plank What is the upward force from the trestle at B at the instant the plank starts to tip g How far is the man from A as the plank tips K 1 m 1 m A weight of man 480 N 2 m centre of mass of plane weight of plank 120 N B

A circular roller of radius 0 5 m is in contact at the top and bottom points of its circumference with two conveyor belts AA and BB as shown in the figure If the belts run at 6 m s and 4 m s both towards right the v and o of the roller A B 1 2 rad s 1 m s 3 2 rad s 5 m s A 6 m s B 4 m s 2 10 rad s 9 m s 4 10 rad s 5 m s

Motion of System of Particles and Rigid Body a 2gh V3 b 3gh 2 4gh V 3 c d gh 139 A disc of mass M and radius R is rolling with angular speed o on a horizontal surface as shown in figure The magnitude of angular momentum of the disc about the origin O is here y is the linear velocity of the disc Iw I MR MR 14 SMR 4 2 MR 00 b MR 0 3 a c MRv d 140 A sphere of mass m and radius r rolls on a horizontal plane without slipping with the speed u Now if it rolls up vertically the maximum height it would attain will be a 3u 4g b 5u 2g c 7u 10g d u 2g MRv 2

beam loaded as shown in the figure below calculate the magnitude of the reaction R of the wall at point B hinged connection and its direction the angle it forms with the horizontal Show all calculations F B 6 ft V 25 A

156 A disc of radius R and thickness R 6 has moment of inertia I 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 a sphere about its diameter is 1 1 32 2 1 64 3 1 5 TC

ABCD is a square frame made of four thin uniform rods each of mass m and length 2 metre If the M the frame about a diagonal BD is 2kg m the mass m of each rod 1 3 kg 2 kg 3 kg

A particle is located at F 01 31 0k in metre A constant force F 01 01 4k in newton begins to act on the particle at t 0 As the particle accelerates under the action of this force the torque acting on particle as measured about the origin Options 1 continuously increases 2 continuously decreases 3 is a non zero constant 4 is always zero

A hollow sphere of radius R moves with initial linear and angular velocities as shown in the figure on a rough horizontal surface The angular velocity of the sphere when its linear velocity becomes zero is O 1 Question Type Single Correct Type V 3V anticlockwise 2 clockwise 3V 3 2R V clockwise

Question 6 If a body is rotating about an axis passing through its centre of mass then its angularmomentum is directed along its a Radius b Tangen c Circumference d Axis of rotation

020 10 0 points There is a moon orbiting an Earth like planet The mass of the moon is 9 25 1022 kg the center to center separation of the planet and the moon is 6 16 105 km the orbital period of the moon is 25 days and the radius of the moon is 1420 km X What is the angular momentum of the moon about the planet 1 5 52257 x 10 4 2 4 71706 x 10 3 3 1 33901 x 10 5 4 1 55846 x 10 4 5 1 7901 x 10 5 6 2 03464 x 10 4 7 9 34725 x 10 3 8 4 23418 x 10 9 1 02101 x 10 5 10 1 47731 x 10 5 2 Answer in units of kg m s

016 part 1 of 2 10 0 points Two ice skaters hold hands and rotate mak ing one revolution in 5 1 s Their masses are 67 kg and 66 kg and they are separated by 2 8 m Find the angular momentum of the system about their center of mass 1 208 273 2 4039 98 3 597 25 4 3368 82 5 1000 55 6 723 823 7 292 634 8 5 67543 9 2810 41 10 321 139

017 part 2 of 2 10 0 points Find the total kinetic energy of the system 1 1337 62 2 1122 94 3 222 55 4 12797 7 5 107 699 6 0 283477 7 188 025 8 624 974 9 535 123 10 197 821 Answer in units of J

Figure shows a disc of mass M and radius R hinged at the centre A small ball of mass M 2 is attached to point P with a thread of length and held at rest at position shown Now the ball is released to fall under gravity with what angular speed the disc starts turning when string becomes taut 10 R P Ball O O R g

2 The moment of inertia of a thin uniform rod rotating about the perpendicular axis passing through one end is I The same rod is bent into a ring and its moment of inertia about the diameter I is I The ratio a 4t 3 I b is 87 3 c 5 3 d 87

The ABC is a triangular plate of uniform thickness The sides are in the ratio shown in the figure IAB IBC and ICA are the moments of inertia of the plate about AB BC and CA respectively Which one of the following relations is correct C A 5 1995 4 3 B AB BC ICA

A sphere of mass M and radius r slips on a rough horizontal plane At some instant it has translational velocity vo and rotational velocity about the centre BVO 2r Find the value of B translational velocity when the sphere starts pure rolling motion found to be v2r

Consider a cylinder of mass M resting on a rough horizontal rug that is pulled out from under it with acceleration a perpendicular to the axis of cylinder What is Ffriction at point P It is assumed that the cylinder does not slip 70 1 2 3 4 Ma Ma 2 Ma 3 Ma V 0 P friction

3 88 A smooth sphere of radius R is made to translate in a straight line with a constant acceleration a g A particle kept on the top of the sphere is released from there at zero velocity with respect to the sphere The speed of particle with respect to the sphere as a function of angle 0 as it slides down is A V Rg sin 0 cos 0 2 C 4Rg sin 0 B Rg 1 cos 8 sin 0 D 2 Rg 1 sin 0 cos 0 3 5 a sm an sp

33 The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is AIPMT Prelims 2011 1 ML 3 TH ML 4 2 A ML2 2

A thin uniform disc of mass M and of radius R A disc of radius passing through O and perpendicular to the plane of disc O 13MR 32 is cut as shown in figure Find the moment of inertia of the remaining disc about an 2 R M

Q 3 Sol A thin and uniform rod of mass M and length L is held vertical on a floor with large friction The rod is released from rest so that it falls by rotating about its contact point with the floor without slipping Which of the following statement s is are correct when the rod makes an angle 60 with vertical g is the acceleration due to gravity A The radial acceleration of the rod s center of mass will be 38 B The angular speed of the rod will be C The angular acceleration of the rod will be Mg D The normal reaction force from the floor on the rod will be 16 A B D To find oo we apply COE 0 2L aCM radial 00 0 1 38 To find o we take torque about A L Mg sin 60 ML a So 3g sin 60 21 L 3g a sin 60 4 thongo ML Mg 1 cos 60 B 60E mg 00

19 A rigid body is to be suspended like a physical pendulum so as to have a time period of T 0 2 second for small amplitude oscillations The minimum distance of the point of suspension from the centre of mass of the body is 1 0 4 m to get this time period Find the maximum distance 1 of a point of suspension from the centre of mass of the body so as to get the same time period g 10 m s 7

A cylinder is pulled without slipping by a string wrapped around it If the string is pulled with a velocity v then 4 points centre of the cylinder moves with a velocity v equal to Your Answer 2v Zero C

A thin uniform rod AB of mass m 1 kg moves translationally with acceleration a 2 m s due to two anti parallel forces F and F The distance between the points at which these forces are applied is equal to 1 20 cm Besides it is known that F 5 N Find the length of the rod A R

Four bodies of masses 5 kg 2 kg 3 kg and 4 kg are respectively placed at positions 0 0 0 2 0 0 0 3 0 and 2 2 0 Calculate the moment of inertia of the system of bodies about x axis y axis and z axis respectively

A uniform rod has mass m 2kg and length 13m One end of the rod is pulled with a constan velocity of v 34m s along a frictionless horizontal floor in the negative x direction The othe end is moving along a parabolic fixed curve The equation of the parabola is x 20y Find th angular velocity of the rod in rad s when the end point B is at 10 5 y axis x 20y 0 0 B 10 5 x axis

Find the ratio of kinetic energy for a purely rolling disc and purely rolling ring if mass of both are same and velocity of centre of mass of disc is double the velocity of centre of mass of ring Question Type Single Correct Type 1 2 3 312 3 2

Answer by appropriately matching the Lists based on the information given in the paragraph A thin uniform rod of mass m and length 1 is free to rotate about a horizontal axis passing through end A The rod is released from rest when it is horizontal at time t 0 aB and ac are accelerations of end point B and mid point C respectively FH is the force by the hinge on the rod g 10 m s and 0 is the angular displacement from initial position a uz neka faut at fad RAI a is on ych Udal ERU OG FRA YUR UN faca sc farHidr 45 444 0 4 1 a ac A Causch RI da FHI g 10 m s Furfuch Rafa chluftu fazu A 1 ag at 0 0 P 25 0 0 RaB List I f II ag at 0 Q 2 5 0 RaB 2 is uf III FH at 0 0 R 1 25 0 0RFH A C IV FH at 0 S 12 5 2 B Question If m C 10 TR F H TT 2 m List II In S I units 1 S I C B T 30 U 15 kg and 2 m then the correct match kg 2 Aan I U II T III S IV R I T II U III S IV R I U II T III R IV S I P II R III U IV S

13 A small mass attached to a string rotates on a frictionless able 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 COT will a decrease by a factor of 2 b remain constant c increase by a factor of 2 d increase by a factor of 4 n TANK A particle of mass m is thrown upwards from the surface of the earth with a velocity u The mass and the radius of the earth are respectively M and R lion due to gravity 11 paths of the two part a c 5 65 3 2 11 Two identical pianc have a fundament increase in the tens occurrence of 6 beat would be a 0 01 c 0 03 12 A thin prism of ar H 1 5 is combine index 1 75 I

The sum of magnitude of two forces is 25 N The resultant of these forces is normal to the smaller force and has a magnitude of 10 N Then the two forces are O O O C 14 5 N 10 5 N 16 N 9 N 13 N 12 N 20N 5 N

One solid cylinder A and another hollow cylinde B are of same mass and same outer radii The moment of inertia about their axis are and respectively such that 1 A B 3 A B 2 A B 4 Data is incomplete

S The net torque about pivot A provided by the forces shown in the figure for L 4 m is 90 N 60 N 60 A L 2 1 90 Nm 3 270 Nm 90 70 N 30 150 N 60 B L 2 2 180 Nm 4 750 Nm 50 N