Rotation Questions and Answers

To determine the location of the center of mass of a car, the car is driven over a scale. When the front wheels are over the scale, the weight recorded by the scale is 5800 N, and when the rear wheels are over the scale, the scale reads 6500 N. The distance between the front and rear wheels is 3.20 m. How far behind the front wheels is the center of mass located? 1.69 m 1.72 m 0.845 m 1.50 m 1.59 m

A potter's wheel moves uniformly from rest to an angular speed of 0.25 rev/s in 35.0 s. (a) Find its angular acceleration in radians per second per second. (b) Would doubling the angular acceleration during the given period have doubled final angular speed?

uniform disc of mass M and radius Ris rotating about its centre of mass (the centre of mass is at rest )with an angular speed w .the angular momentum of disc about a point A (as shown)will be.

Suppose you push with a tangential force of 278 N on the rim of a 40.2 Kg merry-go-round with a radius of 2.2 m. Consider the merry-go-round itself to be a uniform disk with a negligible retarding friction. For the moment of inertia of a disk with uniform distribution of the mass, use Idisk= 1/2mr². Calculate the angular acceleration produced. A. 0.0628 rad/s² B. 62.867 rad/s² C. 6.2867 rad/s² D. None of the above

A rod of mass M and length Z can rotate about a hinge at its left end and is initially at rest. A putty ball of mass m, moving with speed V. strikes the rod at angle 0 from the normal and sticks to the rod after the collision. What is the total moment of inertia, 7, with respect to the hinge, of the rod-ball-system after the collision? What is the angular speed of of the system immediately after the collision, in terms of system parameters and 7?

A mass of 1.4 kg is located at the end of a very light and rigid rod 73 cm in length. The rod is rotating about an axis at its opposite end with a rotational velocity of 3.5 rad/s. (a) What is the rotational inertia of the system? (b) What is the angular momentum of the system?

A torque of 45 N m producing a counterclockwise rotation is applied to a wheel about its axle. A frictional torque of 12 N m acts on the axle. (a) What is the net torque about the axle of the wheel? (b) If the wheel is observed to accelerate at a rate of 6.2 rad/s² under the influence of thesetorques, what is the rotational inertia of the wheel?

A bicycle wheel is rotationally accelerated at a constant rate of 1.3 rev/s². (a) If it starts from rest, what is its rotational velocity after 3 sec? (b) Through how many revolutions does it turn in this time?

A uniform disk with a mass of 8 kg and a radius of 0.4 m is rotating with a rotational velocity of 10 rad/s. (a) What is the rotational inertia of the disk? (b) What is the angular momentum of the disk?

Two 0.6 kg masses are located at either end of a 1 m long, very light and rigid rod as in the diagram. (a) What is the rotational inertia of this system about an axis through the center of the rod?

A weight of 66 N is located a distance of 15 cm from the fulcrum of a simple balance beam. (a) At what distance from the fulcrum should a weight of 19 N be placed on the opposite side in order to balance the system?

Which of the following is not true about a first class lever? The first class levers change direction of the force. The ideal mechanical advantage is <1, = 1, or >1. The fulcrum is located outside of the input and output, closer to the input. The fulcrum is located in between the input and output, in the middle of them.

A string is wrapped around a 6.00-kg cylinder whose radius is 45.0 cm. A weight whose mass is 2.00 kg is attached as shown. The weight is released and begins a downward journey. What is the magnitude of the acceleration of the weight?

A 14.0-kg solid homogeneous disk of radius 0.600 m is rotating with an initial angular speed of 50.0 rad/s about a frictionless horizontal shaft. A 6.00-kg solid homogeneous disk of radius 0.400 m is initially at rest on the same shaft. The disks are pushed into contact, as shown. Because of surface friction, the two disks eventually attain a final common angular speed 404. (a) Find the final common angular speed wy of the system. (b) In the collision of the two disks, kinetic energy is not conserved because nonconservative (frictional) internal forces act during the contact. How much energy was lost to friction in the collision?

How the ratio of output force, Fo, to input force, F, is related to the lengths l and lo from the pivot? Ignore friction and the mass of the lever, and assume the work output equals work input.

(II) A ball of radius r rolls on the inside of a track of radius R (see Fig. 8-53). If the ball starts from rest at the vertical edge of the track, what will be its speed when it reaches the lowest point of the track, rolling without slipping? R 90° R FIGURE 8-53 Problem 57.

Suppose a disk rotates through sixteen revolutions in 7 seconds. (a) What is the displacement in radians in this time? (b) What is the average rotational velocity in rad/s?

A disk of radius 0.25 m is attached at its edge to a light (massless) wire of length 0.50 m to form a physical pendulum. Assuming small amplitude motion, calculate its period of oscillation. For a disk, 1 = (1/2)MR^2 about its center of mass.

An automobile tire with radius 0.50 meters is rolling with an angular velocity of 4 rad/s start to accelerate with a rate of a = 2.3 m/s². a) What is the linear speed at the center of the tire and at the bottom of the tire? b) What is the angular acceleration and centripetal acceleration for a point at the top of the tire?

Two children playing on a frictionless garden gate invent a new game called "gate". The idea is that they will get on opposite sides of the gate and each push such that the gate does not move. If they both push horizontally and perpendicular to the gate and one child pushes with a force of 130 N at a distance of 0.600 m from the hinges, determine the force the second child must exert in order to keep the gate from moving if she pushes at a distance of 0.495 m from the hinges.

A disk of mass M is spinning freely at 6.99 rad/s when a second identical disk, initially not spinning, is dropped onto it so that their axes coincide. In a short time the two disks are corotating. (a) What is the angular speed of the new system (in rad/s)? (b) If a third such disk is dropped on the first two, find the final angular speed of the system (in rad/s).

Each of the following objects has a radius of 0.209 m and a mass of 2.38 kg, and each rotates about an axis through its center (as in this table) with an angular speed of 40.5 rad/s. Find the magnitude of the angular momentum of each object. (a) a hoop (b) a solid cylinder (c) a solid sphere (d) a hollow spherical shell

A 205-kg merry-go-round in the shape of a uniform, solid, horizontal disk of radius 1.50 m is set in motion by wrapping a rope about the rim of the disk and pulling on the rope. What constant force would have to be exerted on the rope to bring the merry-go-round from rest to an angular speed of 0.600 rev/s in 2.00 s? (State the magnitude of the force.) N

A dentist's drill starts from rest. After 3.10 s of constant angular acceleration it turns at a rate of 2.00 x 10* rev/min, (a) Find the drill's angular acceleration. rad/s2 (b) Determine the angle (in radians) through which the drill rotates during this period. rad

A small 290-gram ball on the end of a thin, light rod is rotated in s horizontal circle of radius 12 m Calculate the moment of inertia of the ball about the center of the circle. Express your answer to two significant figures and include the appropriate units. Calculate the torque needed to keep the ball rotating at constant angular velocity If air resistance exerts a force of 0.029 N on the ball, Ignore air resistance on the rod and its moment of inertia. Express your answer to two significant figures and include the appropriate units.

Given two wheels both of mass 4kg and of radius 0.3m. One has all its mass concentrated in a heavy rim and the other is a un thin flat disc. Calculate the rotational kinetic energy of both i are rotated at 10 rev s-¹.

An 88 kg fullback moving east with a speed of 5.0 m/s is tackled by a 97 kg opponent running west at 3.0 m/s, and the collision is perfectly inelastic. What is the speed of the players just after the tackle? (5 points) A. 149 m/s B. 23.1 m/s C. 7.31 m/s D. 0.81 m/s.

Formula Based Problem: Two cars get in a head-on perfectly inelastic collision. The first car was travelling to the right at 25m/s and was 1200kg. The second car was going to the left at 30m/s and was 1400kg. What is the final velocity of the two cars? (Reminder: velocity includes direction)

A manufacturer of CD-ROM drives claims that the player can spin the disc as frequently as 1100 revolutions per minute. If spinning at this rate, what is the speed of the middle row of data on the disc; this row is located 2.8 cm from the center of the disc?

The figures above show three stages of a dive performed by an athlete. During the dive, the athlete completes several rotations in midair while traveling from the platform to the surface of the water. Figure 1 shows the athlete just after jumping off the platform. Figure 2 shows the athlete rotating in midair. Figure 3 shows the athlete about to enter the water. (a) In a clear, coherent paragraph-length response that may also contain figures and/or equations, explain why the athlete's angular speed increases between Figure 1 and Figure 2 but decreases between Figure 2 and Figure 3. (b) is the rotational kinetic energy (K2, rotational) of the athlete in Figure 2 greater than, less than, or equal to the rotational kinetic energy (K1, rotational) of the athlete in Figure 1?

It takes 2000 Nm of torque to loosen a large bolt. You are only powerful enough to apply 620 N of force to the wrench lever. How long does the wrench lever need to be for you to be able to loosen the bolt by applying a perpendicular force? (A) 3.2 m (B) 4.2 m (C) 2.2 m (D) 1.2 m

A disk rotates about an axis through its center. Point A is located on its rim and point B is located exactly one fourth of the way from the center toward the rim. What is the ratio of the angular velocity w A to that of wg, and the tangential velocity VA to that of velocity VB? (a) the angular velocity ωA to that of ωB ωA/ωB= (b) the tangential velocity VA to that of VB VA/VB=

A pulley with a radius of 12 inches uses a belt to drive a pulley with a radius of 35 inches. The 12-inch pulley turns through an angle of 270°. Find the angle (in degrees) through which the 35-inch pulley turns.

If global warming continues, it's likely that some ice from the polar ice caps of the Earth will melt and the water will be distributed closer to the Equator. If this occurs, the length of the day (one rotation) would do which of the following? increase remain the same decrease

A vinyl can turn 10.42 times within 3.46 s. If it starts from rest, what is its angular acceleration? Round your answer to 2 decimal places.

6. A rolling ball will eventually come to rest, even without air resistance, because: a. There is still some friction, even when rolling b. All things naturally come to rest c. The ground is not perfectly level.

A roller coaster (mass of 350. kg) is released from a height of 85 m on a frictionless track. It encounters a loop the loop (at ground level) with a radius= 25 m. What is the velocity at the top of the loop? *

The magnitude of the angular momentum of a 625 g basketball (radius 22.9 cm) spinning at 11 rev/s on an axis through its center of mass is approximately... 0.24 kg m² s-1 0.36 kg m² s-1 0.14 kg m² s-1 38 kg m² s-1

A disk is free to rotate about a fixed axis at its center. If the angular velocity of the disk as a function of time is given by w = 3t4-2t - 6 (in rad/s with t in seconds), find its angular acceleration at t = 3.500 s. 512.5 rad/s² 514.5 rad/s² 437.2 rad/s² 441.0 rad/s²

A hoop, a spherical shell, a solid sphere, and a hollow cylinder, all with the same mass and same radius are released from rest at the top of an incline. If they roll without slipping, which is the first to reach the bottom of the incline? the hoop the spherical shell the solid sphere the hollow cylinder

A thin rod AB of mass M, length 'a' has a variable mass per unit length P0(a+x) / a where x is the distance measured from the end. A and Po is a constant. The rod is freely pivoted at A. The moment of inertia of the rod about an axis passing through A and perpendicular to AB is 7Ma^2/18 5Ma^2/18 Ma^2/12 Ma^2/18

At some instant, a particle is moving along a straight line 2x-3y=2 and its co-ordinates on that line are (4,2) Now at another instant the same particle is moving along a straight line 3x+4y=7 and its co-ordinate are (1,1). The co-ordinates of the axis about which it is in pure rotation are (8/9, 16/9) (5/17,6/17) (30/17,35/17) (50/17,61/17)

In what type of circuit do electrons follow one path from the source, to a load, and back to the source? a) connected circuit b) short circuit c) parallel circuit d) series circuit e) open circuit

We wrap a light, nonstretching cable around a solid cylinder with radius R and moment of inertia I. The cylinder rotates with negligible friction about a stationary horizontal axis. We tie the free end of the cable to a block of mass m and release the block from rest at a distance h above the floor. As the block falls, the cable unwinds without stretching or slipping. Find the speed of the falling block as the block strikes the floor. (m= 2 kg. g = 10 m/s^2, h = 2.5 m, R=4 m, 1 = 64 kg.m^2)

Which of the following statement is true regarding forced oscillation ? If the driving frequency is greater than the frequency of the system then amplitude of the system will be maximum If the driving frequency is greater than the frequency of the system then amplitude of the system will be minimum If the driving frequency is equal to the frequency of the system then amplitude of the system will be minimum If the driving frequency is equal to the frequency of the system then amplitude of the system will be maximum

A 2000 kg solid cube with sides that are 30 cm is rotating around an axis through it's center and perpendicular to two parallel faces of the cube. What is the cube's moment of inertia?

It has been suggested that rotating cylinders about 16.0 mi long and 5.63 mi in diameter be placed in space and used as colonies. What angular speed must such a cylinder have so that the centripetal acceleration at its surface equals the free-fall acceleration on Earth?

What is the torque required to spin a sphere of moment of inertia of 2x104 kgm² to an angular momentum of 3000 kgm²/s in 10 seconds?

A disc of Mass 'M' = 6kg and Radius R = 3m is lying on a horizontal smooth surface free to move. A particle of mass m moving with velocity Vo = 5.2 m/s strikes at the surface tangentially as shown in fig. Calculate velocity (in m/s) of centre of disc (for e = 0)

A 240-kg merry-go-round in the shape of a uniform, solid, horizontal disk of radius 1.50 m is set in motion by wrapping a rope about the rim of the disk and pulling on the rope. What constant force would have to be exerted on the rope to bring the merry-go- round from rest to an angular speed of 0.600 rev/s in 2.00 s? (State the magnitude of the force.) N