Rotation Questions and Answers

29 A 24 5 kg child is standing on the outer edge of a horizontal merry go round that has a moment of inertia of 989 kg m about a vertical axis through its center and a radius of 2 40 m The entire system including the child is initially rotating at 0 180 rev s Find the angular velocity if the child moves to a new position 1 10 m from the center of the merry go round

26 A uniform solid 100 kg cylinder with a diameter of 1 0 m is mounted so it is free to rotate about fixed horizontal frictionless axis that passes through the centers of its circular ends A 10 kg block is hung from very light thin cord wrapped around the cylinder s circumference When the block is released the cord unwinds and the block accelerates downward as shown in the figure What is the acceleration of the block

In outer space two identical space modules are joined together by a massless cable These modules are rotating about their center of mass which is at the center of the cable because the modules are identical see the drawing In each module the cable is connected to a motor so that the modules can pull each other together The initial tangential speed of each module is Vo 19 4 m s Then they pull together until the distance between them is reduced by a factor of eight Each module has a final tangential speed of vf Find the value of Vf

A uniform solid sphere 1 0 4 M R2 of mass M 2 00 kg rolls without slipping on a horizontal surface At the instant its center of mass speed is 10 0 m s the total kinetic energy in Joules is

2 Two masses mand my are suspended on an ornament The ornament is hung from the ceiling at a point which is 10 centimeters from mass my and 30 centimeters from mass m a If m 6 kg what does my have to be for the ornament to be in rotational equilibrium b Calculate the ratio of 1 so that the ornament will be horizontal m c Suppose m 10 kg and m 2 kg You wish to place a third mass m3 5 kg on the ornament to make it balance Should m3 be placed to the right or to the left of the ornament s suspension point Explain your answer Calculate the exact location where me should be plagod 10cm 30cm m

A 25 0 Rg unit ladder of length m leans against a frictionless vertical wall so that it makes an angle of 53 0 degrees with respect to the level floor How large in Newtons is the force exerted on the ladder by the vertical wall a 123 b 92 3 c 490 d 245 e 121

a 2015 Pearson Education Inc a neither as e both Center of mass b only the right one c only the left one d impossible to tell b Center of mass

A hoop I M R starts from rest and rolls without slipping down an incline with h 10 m above a level floor Using the acceleration of gravity as g 10m s2 the translational center of mass speed vcm in m s of the hoop on the level floor is

A 25 0 kg uniform ladder of length 9 00 m leans against a frictionless vertical wall so that it makes an angle of 53 0 degrees with respect to the level floor How does the force of static friction between the level floor and the foot of the ladder compare to the force exerted by the vertical wall on the ladder a the force of static friction must be twice as large b identical in size c the static force of friction must be less d the static force of friction must be half as large e the static force of friction must be larger

out edge of the turl when the al speed the turntable is 9 55 revolutions per minute she has a linear tangential speed of 2 cm s The linear speed of her friend who sits at the edge twice as far from the axis of rotation will be 2015 Pon Education Inc a 2 cm s b 3 14 cm s c 6 cm s a

A 4 0 kg mass located at r 1 5 m i moves with velocity v 2 0 m s j The angular momentum L of this particle with respect to the origin is a 12 kg m s j b none of these C 12 kg m s i d 12 kg m s k e 0

The horizontal bar in the figure will remain horizontal if R R 5 LI M M R M R2 M M M R M R M1L1 M L2 M L2 M L1 L M

4 identical 24 3 gram masses are 12 9 cm from an axis of rotation and rotating at 138 revolutions per minute What is the Rotational Kinetic Energy The strings holding the masses are of negligible mass

4 identical 22 4 gram masses are 10 3 cm from an axis of rotation and rotating at 150 revolutions per minute What is the Rotational Kinetic Energy The strings holding the masses are of negligible mass

4 identical 21 3 gram masses are 6 5 cm from an axis of rotation and rotating at 186 revolutions per minute What is the moment of inertia of the 4 object system The strings holding the masses are of negligible mass

4 identical 18 4 gram masses are 13 cm from an axis of rotation and rotating at 155 revolutions per minute What is the moment of inertia of the 4 object system The strings holding the masses are of negligible mass

If a rotating object decreases in size its rotation rate will speed up What objects did we discuss in class that are the ultimate example of this phenomenon a white dwarfs O b binary stars Oc brown dwarfs d neutron stars

Course Contents Timer Notes Evaluate Feedback HW10 Pivoting Cylinder M a solid cylinder M 2 15 kg R 0 123 m pivots on a thin fixed frictionless bearing A string wrapped around the cylinder pulls downward with a force F which equals the weight of a 0 750 kg mass i e F 7 357 N Calculate the angular acceleration of the cylinder R M

2 A drum of 4 in radius is attached to a disk of 8 in radius The disk and drum have a combined weight of 10 lb and a combined radius of gyration of 6 in A cord is attached as shown and pulled with a force P of magnitude 5 lb Knowing that the coefficients of static and kinetic friction are u 0 25 and p 0 20 respectively determine a whether or not the disk slides b the angular acceleration of the disk and the acceleration of G Figure 2 P

A rigid rod of mass 6 30 kg and length of 3 30 m rotates in a vertical x y plane about nass 1 60kg a friction less pivot through its center Particles m 4 70 kg and m mass are attached at the ends of the rod Determine the size of the angular acceleration of the system when the rod makes an with the horizontal angle of 40 5 in rad 5 2

6 4 rigid rod of mass 6 30 kg and length of 3 30 m rotates in a vertical x y plane about a friction less pivot through its certer Particles in moss 1 60kg mass 4 70 kg and m are attached at the ends of the rod Determine the size of the angular acceleration of the system when the rod makes an with the horizontal angle of 40 5 Cin rad s 2

5 A proposed space station includes living quarters 10 in diameter i A t what so a circular ring 50 5 m angular speed should the ring rotate to the occupants feel that they have the same weight as they they do on Earth

Timer Notes Evaluate Feedback Print Info stands on a platform that is rotating hrw8c11p43 A man stands on a platform that is rotating without friction with an angular speed of 1 4 rev s his arms are outreached and he holds a weight in each hand The otational inertia of the system of man weights and platform about the central axis is 16 00 kg m If by moving the weights the man decreases the rotational inertia of the system to 7 68 kg m what is the resulting angular speed of the platform rad s 2 92 rad s T Submit Answer Incorrect Tries 1 10 Previous Tries What is the ratio of the new kinetic energy of the system to the original kinetic energy Submit Answer Tries 0 10 What provided the added kinetic energy Ofriction O muscles Obrainwaves Oplatform gravity

Timer is the rotational inertia of this collection Notes Evaluate hrw8c10p44 The masses and coordinates of four particles are as follows 30 g x 2 0 cm y 1 0 cm 35 g x 0 0 cm y 4 0 cm 30 g x 3 0 cm y 3 0 cm 30 g x 1 0 Feedback Print Info cm y 5 0 cm What is the rotational inertia of this collection with aspect to the x axis kg m 1 61 104 kg m 2 Computer s answer now shown above You are correct Your receipt no is 159 8739 Previous Tries What is the rotational inertia of this collection with aspect to the y axis 51 10 6 kg m 2 Submit Answer Incorrect Tries 1 10 Previous Tries What is the rotational inertia of this collection with aspect to the z axis 1 61 10 4 kalm 2 Submit Answer Incorrect Tries 2 10 Previous Tries

ml Submit Answer Tries 0 10 ong which axis is the total angular momentum directed 1 5 m 2 2 m s 3 6 m s 2 8 m m2 w8c11p27 Two objects are moving as shown in the figure xy plane Their masses are m1 3 6 kg and m2 3 3 kg at is their total angular momentum about point O

A net torque applied to an object causes a linear acceleration of the object the object to rotate at a constant rate the moment of inertia of the object to change the angular velocity of the object to change

produces more torque: applying the force at an angle of 45° on a wrench that is 0.25 m long or applying the force at an angle of 120° on a wrench that is 0.15 m long?

A child attempts to use a wrench to remove a nut on a bicycle. Removing the nut requires a torque of 20 Nm. The maximum force the child can exert at 80° to the wrench is 40 N. What length of wrench will be needed? A. 0.1 m B. 0.05 m C. 0.2 m D. 0.5 m

A constant torque of 84 N-m applied to a 0.70-kg solid homogeneous disk causes it to rotate about a vertical axis passing through its center, as shown. The diameter of the disk is 4 meters. Find the angular acceleration produced by the torque.

57. (II) A person of mass 75 kg stands at the center of a rotating merry-go-round platform of radius 3.0 m and moment of inertia 820 kg m². The platform rotates without friction with angular velocity 0.95 rad/s. The person walks radially to the edge of the platform. (a) Calculate the angular velocity when the person reaches the edge. (b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person's walk.

22. A solid ball of mass 1.0 kg and radius 10 cm rolls with a forward speed of 10 m/s when it comes to a hill. There is enough friction on the hill to keep the ball from slipping as it rolls up. (a) How high vertically up the hill can the ball roll before coming to rest? (b) How high vertically could the ball go if the hill were totally frictionless? (c) How is it that the ball can go higher with friction than without friction?

Two flywheels of negligible mass and different radii are bonded together and rotate about a common axis (see below). The smaller flywheel of radius 30 cm has a cord that has a pulling force of 50 N on it. What pulling force needs to be applied to the cord connecting the larger flywheel of a radius of 50 cm such that the combination does not rotate? F = ? Round your answer to 2 decimal places.

6. A force of 75 N is applied to a wrench in a counterclockwise direction at 60 to the handle, 12 cm from the centre of a bolt. a) Calculate the magnitude of the torque? b) In what direction does the bolt move? Can you please explain part b) in detail? Is the direction counterclockwise or anticlockwise?

21. A hoop with a mass of 2.75 kg is rolling without slipping along a horizontal surface with a speed of 4.5 m/s when it starts down a ramp that makes an angle of 25° below the horizontal. What is the rotational kinetic energy of the hoop after it has rolled 3.0 m down as measured along the surface of the ramp? O 62 J O 34 J O This question cannot be answered without knowing the radius of the hoop. O 45 J O 22 J

A straight rod of length 'a' is made of an unusual material having mass per unit length u(x)=2x, where is measured from the centre of the rod. The moment of inertia about an axis perpendicular to the rod and passing through one end of the rod is given by (a)λa4/16 (b)3λa4/16 (c)λa4/32 (d)3λa4/32

An 85.5 kg astronaut is training for accelerations that he will experience upon reentry. He is placed in a centrifuge (r = 12.0 m) and spun at a constant angular velocity of 18.4 rpm. Answer the following: (a) What is the angular velocity of the centrifuge in rad / s? (b) What is the linear velocity of the astronaut at the outer edge of the centrifuge? (c) What is the centripetal acceleration of the astronaut at the end of the centrifuge? (d) How many g's does the astronaut experience? (e) What is the centripetal force experienced by the astronaut?

The energy E of a rotating object varies directly as the product of its angular mass I and angular velocity w, and inversely as the square of its radius r. The energy E is 100 J for a angular mass of 2kg m^2, radius 0.5m and angular velocity 10 rad per second. Find the energy for the angular mass 1 kgm^2, radius 0.3 m and angular velocity 5 rad per second.

The period of the mathematical pendulum for a small amplitude (use formula for T0) is 3 seconds on Earth. What is the period of this pendulum (the same length) on the Moon? The acceleration due to gravity on the Moon is 1.6 m/s^2

An athlete whirls a 7.17 kg hammer tied to the end of a 1.4 m chain in a simple horizontal circle where you should ignore any vertical deviations. The hammer moves at the rate of 1.26 rev/s. What is the centripetal acceleration of the hammer? Assume his arm length is included in the length given for the chain. Answer in units of m/s².

Human centrifuges are used to train military pilots and astronauts in preparation for high-g maneuvers. A trained, fit person wearing a g-suit can withstand accelerations up to about 9g (88.2 m/s2) without losing consciousness. (a) If a human centrifuge has a radius of 3.77 m, what angular speed (in rad/s) results in a centripetal acceleration of 9g? rad/s (b) What linear speed (in m/s) would a person in the centrifuge have at this acceleration? m/s

Learning Goal: To understand the meaning of the variables that appear in the equations for rotational kinematics with constant angular acceleration. Rotational motion with a constant nonzero acceleration is not uncommon in the world around us. For instance, many machines have spinning parts. When the machine is turned on or off, the spinning parts tend to change the rate of their rotation with virtually constant angular acceleration. Many introductory problems in rotational kinematics involve motion of a particle with constant nonzero angular acceleration. The kinematic equations for such motion can be written as θ = θo+wot+1/2at² and w=wo + at Here, the meaning of the symbols is as follows: θ is the angular position of the particle at time t. . θo is the initial angular position of the particle. w is the angular velocity of the particle at time t. wo is the initial angular velocity of the particle α is the angular acceleration of the particle Part C True or false: The quantity represented by wo is a function of time (i.e., is not constant). true false Part D True or false: The quantity represented by w is a function of time (i.e., is not constant). true false

IP A ceiling fan is rotating at 1.0 rev/s. When turned off, it slows uniformly to a stop in 2.1 min. Using the result from part A, find the number of revolutions the fan must make for its speed to decrease from 1.0 rev/s to 0.50 rev/s.

Two small balls A and B, each of mass m, are joined rigidly by a light horizontal rod of length L. The rod is clamped at the centre in such a way that it can rotate freely about a vertical axis through its centre. the system is rotated with an angular speed w about the axis. A particle P of mass m kept at rest sticks to the ball A as the ball collides with it. Find the new angular speed of the rod.

1. Verify the equations of rotational motion. Use the value of v from the theory, and time for one case (shape and angle) calculate the final angular velocity Here r is the radius of your object. Then calculate the total angle of the rolling Here t is the average time of the descend. Now, calculate the total circumference of the rolling path This must be equal to the L (linear distance along the incline). Write and compare the two.

A 8.4 N weight is attached 5.8 cm from the fulcrum of a balance beam. What weight should be placed 4.0 cm away from the fulcrum on the other side of the beam in order to balance the system? (Answer in N)

When a figure skater makes a jump, he increases his rotation speed by pulling together his arms and legs. This reduces his rotational inertia causing him to spin faster. If the initial spin rate of a figure skater is 1 RPM and he decreases his rotational inertia by half during the spin, what is his final spin rate? 1 RPM 2 RPM 4 RPM 0.5 RPM

A physics teacher on a spinning chair has a moment of inertia of 4.2 kg m^2 with his arm outstretched. When he pulls his arms in, his moment of inertia is reduced to 1.2 kg m^2. If he starts with arms outstretched with an angular velocity of 14 revolutions-per-minute (rpm), what will his angular velocity be when he pulls in his arms? (Answer in rpm)

An 82.0 kg-diver stands at the edge of a light 5.00-m diving board, which is supported by two pillars 1.60 m apart, as shown in Figure 11-5. Find the force exerted by pillar A.

A solid cylinder of mass 10 kg is pivoted about a frictionless axis thought the center O. A rope wrapped around the outer radius R₁ = 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?

A cable car at a ski resort carries skiers a distance of 7.5 km. The cable which moves the car is driven by a pulley with diameter 4.0 m. Assuming no slippage, how fast must the pulley rotate for the cable car to make the trip in 10 minutes? 60 rpm 9.4 rpm 80 rpm 30 rpm