Physics C Rotational S*** (It made me bleep it) Test

Two blocks are joined by a light string that passes over the pulley shown above, which has radius R and moment of inertia I about its center. T1 and T2 are the tensions in the string on either side of the pulley and a is the angular acceleration of the pulley. Which of the following equations best describes the pulley's rotational motion during the time the blocks accelerate?

(T2-T1)R=l(alpha)

A wheel rotating about a fixed axis has an angular position given by q = 3.0 - 2.0t3, where q is measured in radians and t in seconds. What is the angular acceleration of the wheel at t = 2.0 s?

-24 rad/s^2

A cylinder rotates with constant angular acceleration about a fixed axis. The cylinder's moment of inertial about the axis is 4 kg m2. At time t = 0 the cylinder is at rest. At time t = 2 seconds its angular velocity is 1 radian per second. What is the angular acceleration of the cylinder between t = 0 and t = 2 seconds?

0.5rad/s^2

The rigid body shown in the diagram above consists of a vertical support post and two horizontal crossbars with spheres attached. The masses of the spheres and the lengths of the crossbars are indicated in the diagram. The body rotates about a vertical axis along the support post with constant angular speed w. If the masses of the support post and the crossbars are negligible, what is the ratio of the angular momentum of the two upper spheres to that of the two lower spheres?

1/8

The turntable of a record player has an angular velocity of 8.0 rad/s when it is turned off. The turntable comes to rest 2.5 s after being turned off. Through how many radians does the turntable rotate after being turned off? Assume constant angular acceleration.

10 rad

A 5-meter uniform plank of mass 100 kilograms rests on the top of a building with 2 meters extended over the edge as shown above. How far can a 50-kilogram person venture past the edge of the building on the plank before the plank just begins to tip?

1m

A cylinder rotates with constant angular acceleration about a fixed axis. The cylinder's moment of inertial about the axis is 4 kg m2. At time t = 0 the cylinder is at rest. At time t = 2 seconds its angular velocity is 1 radian per second. What is the kinetic energy of the cylinder at time t = 2 seconds?

2 J

A 2 kg object moves in a circle of radius 4 m at a constant speed of 3 m/s. A net force of 4.5 N acts on the object. What is the angular momentum of the object with respect to an axis perpendicular to the circle and through its center?

24 kg m^2/s

A disk is free to rotate about an axis perpendicular to the disk through its center. If the disk starts from rest and accelerates uniformly at the rate of 3 adians/s2 for 4 s, its angular displacement during this time is

24 radians

A system of two wheels fixed to each other is free to rotate about a frictionless axis through the common center of the wheels and perpendicular to the page. Four forces are exerted tangentially to the rims of the wheels, as shown above. The magnitude of the net torque on the system about the axis is

2FR

A solid cylinder of mass m and radius R has a string wound around it. A person holding the string pulls it vertically upward, as shown above, such that the cylinder is suspended in midair for a brief time interval Dt and its center of mass does not move. The tension in the string is T, and the rotational inertia of the cylinder about its axis is nar007-2.jpg.

2g

A particle of mass m and speed vo collides and sticks to the end of a uniform solid cylinder of mass M and radius R (I = ½ MR2) . If the cylinder is initially at rest and is pivoted about a frictionless axle through its center, what is the final angular velocity of the system after the collision?

2mv0/(2mR+MR)

A force of 15 N acts at the end of a 2.0 m uniform rod that is pivoted about its center of mass. The rod starts from rest and attains an angular velocity of 10.0 rad/s in 2.0 seconds. What is the moment of inertia of the rod? (all answers are in kg.m2)

3

A wheel of radius R and negligible mass is mounted on a horizontal frictionless axle so that the wheel is in a vertical plane. Three small objects having masses m, M, and 2M, respectively, are mounted on the rim of the wheel, as shown above. If the system is in static equilibrium, what is the value of m in terms of M ?

3M/2

To weigh a fish a person hangs a tackle box of mass 3.5 kilograms and a cooler of mass 5 kilograms from the ends of a uniform rigid pole that is suspended by a rope attached to its center. The system balances when the fish hangs at a point 1/4 of the rod's length from the tackle box. What is the mass of the fish?

3kg

A cylinder of mass M and radius R. whose moment of inertia about its center is (1/2)MR^2, rolls without slipping along a level surface at speed v. The maximum vertical height to which it can roll if it ascends an incline is

3v^2/4g

A cylinder rotates with constant angular acceleration about a fixed axis. The cylinder's moment of inertial about the axis is 4 kg m2. At time t = 0 the cylinder is at rest. At time t = 2 seconds its angular velocity is 1 radian per second. What is the angular momentum of the cylinder at time t = 2 seconds?

4 kg m^2/s

A particle is moving in a circle of radius 2 meters according to the relation q = 3t2 + 2t, where q is measured in radians and t in seconds. The speed of the particle at t = 4 seconds is

52 m/s

A particle moves in the xy-plane with coordinates given by x = Acoswt and y = Asinwt, where A = 1.5 meters and w = 2.0 radians per second. What is the magnitude of the particles acceleration?

6.0m/s^2

In which of the following diagrams is the torque about point O equal in magnitude to the torque about point X in the diagram above? (All forces lie in the plane of the paper.)

60 degree angle, 2F force

A bowling ball of mass M and radius R. whose moment of inertia about its center is (2/5)MR2, rolls without slipping along a level surface at speed v. The maximum vertical height to which it can roll if it ascends an incline is

7v^2/10g

Which arrangement of particles, all of mass m, has the smallest moment of inertia? They are all free to rotate in the plane of the page and the axis of rotation is perpendicular to the page at the point marked by the "x".

A - 3 seperate parts

Two cylinders made of the same material roll down an inclined plane that is inclined at an angle q with the horizontal. They start from rest. They have the same mass, but the radius of cylinder B is twice the radius of cylinder A (B is a shorter cylinder). In what order do they reach the bottom?

A reaches the bottom first because it has a smaller moment of inertia

A square piece of plywood on a horizontal tabletop is subjected to the two horizontal forces shown above right. Where should a third force of magnitude 5 newtons be applied to put the piece of plywood into equilibrium?

A- top right corner pointing down

A satellite of mass M moves in a circular orbit of radius R with constant speed v. True statements about this satellite include which of the following? I. Its angular speed is v/R. II. Its tangential acceleration is zero III. The magnitude of its centripetal acceleration is constant.

All three

A 5-kilogram sphere is connected to a 10-kilogram sphere by a rigid rod of negligible mass, as shown above. Which of the five lettered points represents the center of mass of the sphere-rod combination?

B - to the left of center

Two objects, of masses 6 and 8 kilograms, are hung from the ends of a stick that is 70 centimeters long and has marks every 10 centimeters, as shown above. If the mass of the stick is negligible, at which of the points indicated should a cord be attached if the stick is to remain horizontal when suspended from the cord?

D - just to the right of the center

The graphs below show angular velocity as a function of time. In which one is the magnitude of the angular acceleration constantly decreasing?

E

A 5-kilogram sphere is connected to a 10-kilogram sphere by a rigid rod of negligible mass, as shown above. The sphere-rod combination can be pivoted about an axis that is perpendicular to the plane of the page and that passes through one of the five lettered points. Through which point should the axis pass for the moment of inertia of the sphere-rod combination about this axis to be greatest?

E - far right

A uniform stick has length L. The moment of inertia about the center of the stick is Io. A particle of mass M is attached to one end of the stick. The moment of inertia of the combined system about the center of the stick is

I0+(1/4)ML^2

A uniform stick has length L. The moment of inertia about the center of the stick is Io. A particle of mass M is attached to one end of the stick. The moment of inertia of the combined system about the center of the stick is Select one:

I0+(1/4)ML^2

An ant of mass m clings to the rim of a flywheel of radius r, as shown above. The flywheel rotates clockwise on a horizontal shaft S with constant angular velocity w. As the wheel rotates, the ant revolves past the stationary points I, II, III, and IV. The ant can adhere to the wheel with a force much greater than its own weight. It will be most difficult for the ant to adhere to the wheel as it revolves past which of the four points?

III - bottom of wheel

A wheel with rotational inertia I is mounted on a fixed, frictionless axle. The angular speed w of the wheel is increased from zero to wf in a time interval T. 1. What is the average net torque on the wheel during this time interval?

Iwf/T

A wheel with rotational inertia I is mounted on a fixed, frictionless axle. The angular speed w of the wheel is increased from zero to wf in a time interval T. What is the average power input to the wheel during this time interval?

Iwf^2/2T

A figure skater is spinning on frictionless ice with her arms fully extended horizontally. She then drops her arms to her sides. Which of the following correctly describes her rotational kinetic energy and angular momentum as her arms fall? Rotational Kinetic Angular Energy Momentum

KE - Increases AM - Constant

Which of the following quantities is a scalar that is always positive or zero?

Kinetic Energy

A long board is free to slide on a sheet of frictionless ice. As shown in the top view above, a skater skates to the board and hops onto one end, causing the board to slide and rotate. In this situation, which of the following occurs?

Linear Momentum and angular momentum are both conserved

A rod on a horizontal tabletop is pivoted at one end and is free to rotate without friction about a vertical axis, as shown above. A force F is applied at the other end, at an angle q to the rod. If F were to be applied perpendicular to the rod, at what distance from the axis should it be applied in order to produce the same torque?

Lsinq

A rod of negligible mass is pivoted at a point that is off-center, so that length l 1 is different from length l2. The figures above show two cases in which masses are suspended from the ends of the rod. In each case the unknown mass m is balanced by a known mass, M1 or M2, so that the rod remains horizontal. What is the value of m in terms of the known masses?

M1+M2

A wheel of mass M and radius R rolls on a level surface without slipping. If the angular velocity of the wheel is w, what is its linear momentum?

MwR

The bar shown above is pivoted about one end and is initially at rest in a vertical position. The bar is displaced slightly and as it falls it makes an angle q with the vertical at any given time, as shown above. Which of the following graphs best represents the bar's angular velocity w as a function of time?

Positive Increasing Slope

The bar shown above is pivoted about one end and is initially at rest in a vertical position. The bar is displaced slightly and as it falls it makes an angle q with the vertical at any given time, as shown above. Which of the following graphs best represents the bar's angular acceleration a as a function of angle q?

Positive decreasing slope

A figure skater goes into a spin with arms fully extended. Which of the following describes the changes in the rotational kinetic energy and angular momentum of the skater as the skater's arms are brought toward the body? Rotational Angular Kinetic Energy Momentum

RKE - Increase Angular Momentum - Remains same

A uniform ladder of weight W leans without slipping against a wall making an angle q with a floor as shown above. There is friction between the ladder and the floor, but the friction between the ladder and the wall is negligible. The magnitude of the normal force exerted by the floor on the ladder is

W

A uniform ladder of weight W leans without slipping against a wall making an angle q with a floor as shown above. There is friction between the ladder and the floor, but the friction between the ladder and the wall is negligible. The magnitude of the friction force exerted on the ladder by the floor is

W/2 Cot(theta)

A satellite of mass M moves in a circular orbit of radius R with constant speed v. True statements about this satellite include which of the following? I. Its angular speed is v/R. II. Its tangential acceleration is zero III. The magnitude of its centripetal acceleration is constant.

all three

For the wheel-and-axle system shown above, which of the following expresses the condition required for the system to be in static equilibrium?

am1 = bm2

A student initially stands on a circular platform that is free to rotate without friction about its center. The student jumps off tangentially, setting the platform spinning. Quantities that are conserved for the student-platform system as the student jumps include which of the following? I. Angular momentum II. Linear momentum III. Kinetic energy

angular momentum

A light rigid rod with masses attached to its ends is pivoted about a horizontal axis as shown above. When released from rest in a horizontal orientation, the rod begins to rotate with an angular acceleration of magnitude

g/7l

Which of the following quantities is a scalar that is always positive or zero?

kinetic answer

A particle of mass m moves with a constant speed v along the dashed line y = a. When the x-coordinate of the particle is xo, the magnitude of the angular momentum of the particle with respect to the origin of the system is

mva

An ant of mass m clings to the rim of a flywheel of radius r, as shown above. The flywheel rotates clockwise on a horizontal shaft S with constant angular velocity w. As the wheel rotates, the ant revolves past the stationary points I, II, III, and IV. The ant can adhere to the wheel with a force much greater than its own weight. What is the magnitude of the minimum adhesion force necessary for the ant to stay on the flywheel at point III?

mw^2r+mg

A stone falls from rest from the top of a building as shown above. Which of the following graphs best represents the stone's angular momentum L about the point P as a function of time?

positive constant slope

The graphs below show angular velocity as a function of time. In which one is the magnitude of the angular acceleration constantly decreasing?

positive decreasing slope

A sphere of mass M, radius r, and rotational inertia I is released from rest at the top of an inclined plane of height h as shown above. If the plane has friction so that the sphere rolls without slipping, what is the speed vcm of the center of mass at the bottom of the incline?

sqrt((2mghr^2)/(I+mr^2)

A sphere of mass M, radius r, and rotational inertia I is released from rest at the top of an inclined plane of height h as shown above. If the plane is frictionless, what is the speed vcm of the center of mass of the sphere at the bottom of the incline?

sqrt(2gh)

A turntable that is initially at rest is set in motion with a constant angular acceleration a. What is the angular velocity of the turntable after it has made one complete revolution?

sqrt(4pi(alpha))

A uniform rigid bar of weight W is supported in a horizontal orientation as shown above by a rope that makes a 30° angle with the horizontal. The force exerted on the bar at point O, where it is pivoted, is best represented by a vector whose direction is which of the following?

up and to the right

A car travels forward with constant velocity. It goes over a small stone, which gets stuck in the groove of a tire. The initial acceleration of the stone, as it leaves the surface of the road, is

vertically upwards

A solid cylinder of mass m and radius R has a string wound around it. A person holding the string pulls it vertically upward, as shown above, such that the cylinder is suspended in midair for a brief time interval Dt and its center of mass does not move. The tension in the string is T, and the rotational inertia of the cylinder about its axis is (1/2)MR^2 The net force on the cylinder during the time interval Dt is

zero