Rotation Questions and Answers

4 Points DETAILS SERCP11 7 3 OP 007 b What is the angular speed of the wheels in rad s when the linear speed of the bicyclist reaches 10 4 m s rad s Starting from rest a person pedals a bicycle such that the angular acceleration of the wheels is a constant 1 50 rad s2 The bicycle wheels are 36 0 cr a What is the magnitude of the bicycle s linear acceleration in m s m s c How many radians have the wheels turned through in that time rad MY NOTES A

Pin L M Problem 1 A long uniform rod of length L and mass M is pivoted about a frictionless horizontal pin through one end The rod is nudged to the right from rest in a vertical position as shown in the figure above on the left The moment of inertia of the rod about the pin is I MI2 At the instant the rod is horizontal find its angular speed w Answer w 3g L Problem 2 A string is wound around a uniform disk of radius R and mass M The disk is released from rest with the string vertical and its top end tied to a fixed bar see figure above on the right The moment of inertia of a disk is IMR and as the disk descends it rolls without slipping v R What is the the speed of the center of mass of the disk after the disk has descended through a distance b

Wheel 2 has twice the radius of wheel 1 Each is accelerated from rest with a force applied as shown Assume that all the mass of the wheels is concentrated in the rims so that the moment of inertia of each is of the form I M R2 hoop formula In order to impart identical angular accelerations to both wheels how much larger is F than F Recall that T I a O F F O F 8F O F 8F O F 2F O F 4F O F 4F F 2E F2 2F Wheel 1 radius R mass M a 2R Wheel 2 radius 2R mass M

3 A disk released from the top of an in clined plane has a speed of 3 92 mls at the bottom Has high is the upper end the inclined plane I Assume that the dist rolled without slipping in m

X the a Find the centroid 2 pts b Find the moment of inertia about the horizontal X X centroidal axis 5 pt c Find the moment of inertia about the vertical Y Y centroidal axis 4 pts Y 2 Y 6 X 10

1973M3 A ball of mass m is attached by two strings to a vertical rod as shown above The entire system rotates at constant angular velocity to about the axis of the rod a Assuming an is large enough to keep both strings taut find the force each string exerts on the ball in terms of 0 m g R and 0 b Find the minimum angular velocity for which the lower string barely remains taut

0 5 m r 1 5 m Axle Y m 20 kg m C1991M2 Two masses m and m are connected by light cables to the perimeters of two cylinders of radii r and 12 respectively as shown in the diagram above with r 0 5 meter r 1 5 meters and m 20 kilograms a Determine m such that the system will remain in equilibrium

200 2 2 Problem 1 A sphere of radius r 0 12 m and mass m 8 kg starts at rest from the top of an inclined plane with angle and height h 1m The moment of inertia of a sphere is I mr and the sphere rolls without slipping v rw down the inclined plane What is the speed of the sphere when it reaches the bottom of the inclined plane Initial v 0 h 0 Final V jw I

A single force acts on a particle P Rank each of the orientations of the force shown below according to the magnitude of the time rate of change of the particle s angular momentum about the point O least to greatest 1 1 2 3 4 P O 1 and 2 tie then 4 3 All are the same O O 1 and 2 tie then 3 and 4 tie O 1 and 2 tie then 3 4 2 P 3 P 4 P

Q2 A 3kg thin spherical shell with a 0 1m radius is wounded by a string The shell begins at rest before the string is pulled and causes it to spin The string is pulled with 8N at a 0 30 angle to the radius for t 4s a Calculate the torque produced by the tension in the string 3pts b What is the angular acceleration that the spherical shell will experience 3pts c Assuming 0 0 what is the total angle that the shell will rotate during the 4 seconds 3pts d What is the final angular velocity the shell spins at 3pts

A sphere a hoop and a cylinder all with the same mass M and same radius R are rolling along all with the same speed v Isphere MR Idisk MR Ihoop MR Which has the most kinetic energy Sphere O Sphere Disk Qu 8 O All have the same Kinetic Energy

Q1 A set of masses rests on an x y plane measured in meters The masses are m 1kg at 2 1 m 1kg at 2 1 m3 2kg at 0 1 Use the image to answer the following questions m 3 2 1 m3 1 a What is the center of mass in the horizontal direction 3pts b What is the center of mass in the vertical direction 3pts m c What is the inertia of the system if it rotates around the origin 3pts d Calculate the inertia of the system if it rotates around the y axis 3pts 3

4 Modern hard drives spin very fas called the platter Assume an aluminum platter that is 3 5 in in diameter 1 mm thick and spinning at 5400 rpm Treat the platter as a solid disk don t worry about the hole in the middle 4a 1 1 point graded What is the angular momentum of the platter in kg m s when it is spinning at full speed 0 0095 0 0095 Answer 0 009353 Submit You have used 1 of 3 attempts Answers are displayed within the problem Save Show answer 4b 1 point possible graded You are a 70 kg astronaut floating at rest in zero gravity holding your laptop Your hard

A child stands on the edge of a merry go round which spins without friction The child slowly walks towards the center of the platform As the child moves toward the center the platform s rotation rate O can t be determined Ostay the same O increases O decreases

In the figure point P is at rest when it is on the x axis The time t when P returns to the original position on the x axis is closest to 13 s O 18 s 25 s 35 s 50 s D 2 0 m 0 010 rad s

A janitor opens a 1 35 m wide door by pushing on it with a force of 31 5 N directed perpendicular to its surface HINT a What magnitude torque in N m does he apply about an axis through the hinges if the force is applied at the center of the door N m b What magnitude torque in N m does he apply at the edge farthest from the hinges N m

A janitor opens a 1 10 m wide door by pushing on it with a force of 36 5 N directed perpendicular to its surface HINT a What magnitude torque in N m does he apply about an axis through the hinges if the force is applied at the center of the door N m b What magnitude torque in N m does he apply at the edge farthest from the hinges N m

A 156 kg object is moving in a circular path r 10 cm at a constant rate of 8 25 rev s Find the tangential velocity Round your answer to 2 decimal places

A vinyl can turn 8 54 times within 2 85 s If it starts from rest what is its angular acceleration Round your answer to 2 decimal places

A skater is spinning with an angular velocity of 15 rad s She then comes to a stop over a brief period of time During this time her angular displacement is 5 1 rad Determine the time during which she comes to rest Round your answer to 2 decimal places

A fan takes 2 00 s to reach its operating angular speed of 10 0 rev s What is the average angular acceleration rad s 2 Round your answer to 1 decimal place

A car s wheel whose radius is 43 69 cm starts from rest and accelerates uniformly to a velocity of 15 25 m s within 8 77 s Find the number of rotations one wheel makes in the given time interval Round your answer to 2 decimal places

A rod of mass M 9 kg and l 1 m is initially at rest and it is pivoted about one of its ends A mass m 0 004 kg is moving with a speed vo 2300 m sec towards the rod at a distance d 0 5 m from the pivot The mass m then gets embedded in the mass m and the system begins to rotate about the pivot after the collision What is the angular speed w of the m M system after the collision The moment of inertia of a rod about one of its ends is I M and the moment of inertia of a particle is I mr Hint Angular Momentum is conserved about the pivot Initial Final m d Vo O 1 5 rad sec O 3 5 rad sec 5 5 rad sec 075nd rec pivot M l d pivot M me W

The 2 0 m long 15 kg beam in figure is hinged at its left end It is falling rotating clockwise under the influence of gravity and the figure shows its position at 3 different times Express only the numerical portion of the answer and indicate whether the sign is positive or negative a What is the gravitational torque on the beam about an axis through the hinged end when the beam is in the middle position b What is the sign of the torque Write positive or negative 2 0 m 450 20 k

A solid cylinder of radius r 1 m and mass m 1 kg starts at rest from the top of an inclined plane with angle and height h 5 m The moment of inertia of a solid cylinder is I mr and the solid cylinder rolls without slipping v rw down the inclined plane What is the speed of the solid cylinder when it reaches the bottom of the inclined plane Initial v 0 h 7 0 m sec O 8 1 m sec 8 4 m sec 9 0 m sec 0 Final V 3

P 71 0 2 m 0 4 m P 0 25 m 0 35 m 29 18 P3 F2 250 N F3 392 N Problem 4 a Four forces are applying torques on a bar as shown in the figure above What is the net Corque about point P on the bar due to the four forces In which direction will the bar rotate about Doint P CCW or CW Answer Thet 75 6 N m CW b Four forces are applying torques on a bar as shown in the figure above What is the net torque about Doint P2 on the bar due to the four forces In which direction will the bar rotate about point P CCW or CW Answer Thet 10 8 N m CCW c Four forces are applying torques on a bar as shown in the figure above What is the net torque about point P3 on the bar due to the four forces In which direction will the bar rotate about point P3 CCW

Problem 2 In the figure below a rope with tension T is connected to a mass m 0 5 kg The rope then goes over a cylindrical pulley with radius r 0 57 m and moment of inertia I The rope is then connected to mass m2 1 1 kg and the rope now has a tension T The coefficient of kinetic friction between my and the table is 0 1 The acceleration of the system is a 3 m sec and the pulley rotates without slipping a ra a What is the tension T b What is the tension T c What is the moment of inertia of the pulley I a m k T g T

fk T2 m a a m T2 m a Problem 5 In the figure above on the left a rope with tension T is connected to a mass m 1kg The rope then goes over a cylindrical pulley of mass m 0 1 kg and radius r 0 2 m The moment of inertia of a cylinder is I mpr The rope is then connected to mass m 0 5 kg and the re now has a tension T The coefficient of kinetic friction between m and the table is 0 1 What are the tensions T and T and what is the acceleration a of the system Answer a 2 53 m sec T 3 51 N T 3 64 N 4 kg Problem 6 In the figure above on the right a rope with tension Ti is connected to a mass m1 The rope then goes over a cylindrical pulley with radius 0 16 m and moment of inertia 0 38 kg m The moment of inertia of a cylinder is I m r The rope is then connected to mass m 2 kg and the rope now has a tension T2 What are the tensions T and T and what is the acceleration a of the system Answer a 0 94 m sec T 35 44 N T 21 48 N

B B A B AB sin 0 7 7x F T rF sin 0 Tnet Ia a ra Problem 1 Three forces are applying torques on a bar as shown in the figure below a What is the net torque on the bar about point P due to the three forces In which direction will the bar rotate about point P CCW or CW b What is the net torque on the bar about point P2 due to the three forces In which direction will the bar rotate about point P CCW or CW c What is the net torque on the bar about point P3 due to the three forces In which direction will the bar rotate about point P3 CCW or CW P F 41 51 N 55 0 6 m P 0 1 m F3 50 77 N 71 20 0 3 m F 32 17 N P3

Two people of different masses are holding identical bowling balls and are balanced on a seesaw Assuming the larger person does not move then in order to balance after they both drop their bowling balls the smaller person a will not need to adjust their position b will need to move closer to the fulcrum c will need to mover further from the fulcrum d will need to move but the direction depends on the mass of the bowling ball

Consider the following three objects each of the same mass and radius 1 a solid sphere 2 a solid disk 1 0 4MR2 1 0 5MR 3 a hoop 1 MR2 4 All three are released from rest at the top of an inclined plane The three objects proceed down the incline undergoing rolling motion without slipping In which order do the objects reach the bottom of the incline 2 3 1 All three reach the bottom at the same time 1 2 3 3 2 1 3 12

A 2 0 kg hoop 1 MR2 rolls without slipping on a horizontal surface so that its center proceeds to the right with a constant linear speed of v 7 0 m s The radius of the hoop is 0 50 m 72 J 54 J 140 J 49 J What is the total kinetic energy of the hoop 98 J 2 0 kg 4 v

A uniform solid disk 1 0 5MR2 of radius 1 60 m and mass 2 30 kg rolls without slipping starting from rest to the bottom of an inclined plane If the angular velocity of the disk is 5 90 rad s at the bottom what is the height of the inclined plane g 9 80 m s2 4 55 m 8 16 m 5 10 m 6 82 m 5 98 m

A 60 0 kg skater begins a spin with an angular speed of 6 0 rad s By changing the position of her arms the skater decreases her moment of inertia to one half its initial value What is the skater s final angular speed 6 0 rad s 3 0 rad s 4 5 rad s 12 rad s

A force of F 68 0 N is applied tangentially to a wheel of radius R 0 600 m and gives rise to an angular acceleration of 1 90 rad s Calculate the rotational inertia of the wheel in Sl units Your Answer k R fixed axis

A boy and a girl are riding on a merry go round that is turning The boy is twice as far as the girl from the merry go round s center If the boy and girl are of equal mass which statement is true about the boy s moment of inertia with respect to the axis of rotation The moment of inertia is the same for both The boy s moment of inertia is twice the girl s The boy has a smaller moment of inertia but it is impossible to say exactly how much smaller The boy s moment of inertia is 4 times the girl s The boy s moment of inertia is half of the girl s

Two points are located on a rigid wheel that is rotating with decreasing angular velocity about a fixed axis Point A is located on the rim of the wheel and point B is halfway between the rim and the axis Which one of the following statements concerning this situation is true A A B Both points have the same tangential acceleration Each second point Ans through a greater angle than point B Both points have the same instantaneous angular velocity Both points have the same centripetal acceleration The angular velocity at point A is greater than that of point B

A wheel starts from rest and has an angular acceleration of 4 70 rad s2 When it has made 3 00 rev its angular velocity in rad s is Your Answer

O 5 0 rad 10 rad 7 5 rad F A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought the center O A rope wrapped around the outer radius R 1 0 m exerts a force F1 6 0 N to the right A second rope wrapped around another section of radius R2 0 50 m exerts a force F2 6 0 N downward How many radians does the cylinder rotate through in the first 5 0 seconds if it starts from rest 13 rad R1 O FIGURE 8 1

nrw8c11p51 Two skaters each of mass 80 kg approach each other along parallel paths separated by 7 7 m They have equal and opposite velocities of 2 1 m s The first skater carries me end of a long pole with negligible mass and the second skater grabs the other end of it as she passes see the figure Assume frictionless ice Describe quantitatively the motion of he skaters after they have become connected by the pole What is their angular speed Submit Answer Tries 0 8 y pulling on the pole the skaters reduce their separation to 1 0 m What is their angular speed then Submit Answer Tries 0 8 alculate the ratio of the final kinetic energy to the original kinetic energy

An object s angular acceleration is 36 rad s If it were initiall spinning with a velocity of 6 0 m s what would its angular velocity after 5 0 s 4 a 186 rad s b 190 rad s c 174 rad s d 174 rad s

hrw8c11p21 What is the net torque about the origin on a flea located at coordinates 0 m 6 m 3 m when forces F1 3 k and F2 2 M j act on the flea i component torque Submit Answer Tries 0 8 j component of torque Submit Answer Tries 0 8 k component of torque

60 hrw8c11p55 A uniform thin rod of length 0 65 m and mass 3 5 kg can rotate in a horizontal plane about a vertical axis through its center The rod is a rest when a 3 0 in the horizontal plane of the rod is fired into one end of the rod As viewed from above the direction of the bullet velocity makes an angle of 60 with the rod see the fi bullet lodges in the rod and the angular velocity of the rod is 12 0 rad s immediately after the collision what is the magnitude of the bullet s velocity just before impact Submit Answer Tries 0 8

A square metal plate 0 18 m on each side is pivoted about in axis through point 0 at its center and perpendicular to he plate Calculate the net orque about this axis due to he three forces shown if the magnitudes of the forces are 18 N F2 26 N and F3 4 N The plate and all forces are in the plane of the page 0 180 m 0 180 m 45 F

Course Contents HW11 A constant horizonta e hrw8c11p7 A constant horizontal force of 11 0 N is applied to a wheel of mass 10 0 kg and radius 0 40 m as shown in the figure The wheel rolls without slipping on the horizontal surface and the acceleration of its center of mass is 0 715 m s What is the magnitude of the frictional force on the wheel Submit Answer Tries 0 101 What is the rotational inertia of the wheel about an axis through its center of mass and perpendicular to the plane of the wheel SpectrumSetup FO Internet access

Course Contents HW11 Calculate the torque exerted by the friction on the wheel Timer hrw8c11p82 A wheel of radius 0 290 m which is moving initially at 41 m s rolls to a stop in 285 m Calculate its linear acceleration magnitude only Submit Answer Tries 0 10 Calculate its angular acceleration magnitude only Submit Answer Tries 0 10 The wheel s rotational inertia is 0 105 kg m about its central axis Calculate the torque exerted by the friction on the wheel about the central axis N m magnitude only

The unstable truss system has three pin connected steel members If member AB has an angular velocity of w 30 rad s determine the angular velocities of the other members B 100 mm A 260 mm 180 mm C 180 mm D

Rasheed and Sofia are riding a merry go round that is spinning steadily Sofia is twice as far from the axis as is Rasheed Sofia s angular velocity is that of Rasheed half the same as twice R four times we can t say without knowing their radii

When a fan is turned off its angular speed decreases from 10 rad s to 6 3 rad s in 3 3 s What is the magnitude of the average angular acceleration of the fan 3 1 rad s2 0 27 rad s 1 1 rad s 0 74 rad s

A fan is rotating with an angular velocity of 11 rad s You turn off the power and it slows to a stop while rotating through angle of 6 6 rad a Determine its angular acceleration rad s b How long does it take to stop rotating S