Rotational Motion Test - AP Physics I
An ice skater is spinning about a vertical axis with arms fully extended. If the arms are pulled in closer to the body, in which of the following ways are the angular momentum and kinetic energy of the skater affected? - AM: Increases, KE: Increases - AM: Increases, KE: Remains Constant - AM: Remains Constant, KE: Increases - AM: Remain Constant, KE: Remains Constant
- AM: Remains Constant, KE: Increases
A cylinder at rest is released from the top of a ramp, as shown above. The ramp is 1.0 m high, and the cylinder rolls down the ramp without slipping. At the bottom of the ramp, the cylinder makes a smooth transition to a small section of a horizontal table and then travels over the edge at a height of 1.0 m above the floor, eventually landing on the floor at a horizontal distance of 1.5 m from the table. After the cylinder leaves the table, but before it lands, how do the rotational kinetic energy and translational kinetic energy of the cylinder change, if at all? - RKE stays the same, TKE increases - RKE increases, TKE increases - RKE stays the same, TKE stays the same - RKE increases, TKE stays the same
- RKE stays the same, TKE increases
A bicycle wheel of known rotational inertia is free to rotate about its central axis. With the wheel initially at rest, a student wraps a string around the wheel and pulls the string with a spring scale, causing the wheel to rotate. The students records the tension in the string and the time for which the string was pulled. Without measuring the wheel's final angular speed, can the student find the magnitude of the wheel's final angular momentum, and what is a correct explanation? - Yes. the student has sufficient information already - Yes. The student also needs to measure the wheel's radius to calculate the torque exerted on the wheel. - No. Angular momentum can only be found by measuring rotational inertia and angular speed. No. Measuring the radius would allow the student to calculate the torque, not the angular momentum.
- Yes. The student also needs to measure the wheel's radius to calculate the torque exerted on the wheel.
A solid sphere and a solid cylinder, both uniform and of the same mass and radius, roll without slipping at the same forward speed. It is correct to say that the total kinetic energy of the solid sphere is - more than the total kinetic energy of the cylinder - less that the total kinetic energy of the cylinder - equal to the total kinetic energy of the cylinder - impossible to tell
- less that the total kinetic energy of the cylinder
two identical metal spheres are placed at the top of a wooden ramp and then released. Sphere 1 has been oiled, and it slides down without rolling. Sphere 2 has not been oiled, and it rolls down, since friction prevents it from sliding. Which sphere will reach the bottom of the ramp first? - sphere 1 will reach the bottom of the ramp first - it depends on the mass of the spheres - the two reach the bottom at the same time - sphere 2 will reach the bottom of the ramp first
- sphere 1 will reach the bottom of the ramp first
The figure above shows a rod that is fixed to a horizontal surface at pivot P. The rod is initially rotating without friction in the counterclockwise direction. At time t, three forces of equal magnitude are applied to the rod as shown. Which of the following is true about the angular speed and direction of rotation of the rod immediately after time t? - w: increasing, direction: counterclockwise - w: increasing, direction: clockwise - w: decreasing, direction: clockwise - w: decreasing, direction: counterclockwise
- w: decreasing, direction: counterclockwise
A student holds one end of a string in a fixed position. A ball of mass 0.2 kg attached to the there'd of the string moves in a horizontal circle of radius 0.5 m with a constant speed of 5 m/s. How much work is done by the ball by the string during each revolution? - 0 J - 0.5 J - 1.0 J - pi J
0 J
A mechanic is examining the wheel of a bicycle to adjust the brake. With the bicycle off the ground, he manually rotates the wheel until it reaches an angular speed of 12.0 rad/s and then allows it to coast to a stop. If the wheel has a moment of inertia of 0.100 kg m2, and the wheel slows uniformly to a stop in 160 s, what is the magnitude of the retarding torque? - 0.0075 Nm - 1.0 Nm - 1.3 Nm - 1.7 Nm
0.0075 Nm
Mass m = 260 g and mass M = 320 g are attached to a rod of negligible mass as shown in the diagram. Distance d = 60.0 cm and distance s = 40.0 cm. What is the moment of inertia when the masses rotate about the indicated axis of rotation? - 0.15 kgm^2 - 0.21 kgm^2 - 17 kgm^2 - 140 kgm^2
0.15 kgm^2
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 kgm^2 about a vertical axis through its center and a radius of 2.40 m. The entire system (including the child) is intially rotating at 0.180 rad/s. Find the angular veolcity if the child moves to a new position 1.10 m from the center of the merry-go-round. - 0.165 rad/s - 0.175 rad/s - 0.185 rad/s - 0.200 rad/s
0.200 rad/s
A 40.0 kg child running at 3.00 m/s suddenly jumps onto a stationary playground merry-go-round at a distance of 1.50 m from the axis of rotation of the merry-go-round. The child is travelling tangential to the edge of the merry-go-round just before jumping on. The moment of inertia about its axis of rotation is 600 kgm^2 and very little friction at its rotation axis. What is the angular speed of the merry-go-round just after the child has jumped onto it? - 0.261 rad/s - 0.788 rad/s - 2.00 rad/s - 3.14 rad/s
0.261 rad/s
What is the kinetic energy of a 120.0 cm thin uniform rod (I = 1/12mr^2) with a mass of 450.0 g that is rotating around its center at 3.60 rad/s? - 0.350 J - 0.700 J - 0.960 J - 2.10 J
0.350 J
A uniform solid cylinder of mass 10 kg can rotate about a frictionless axle through its center O, as shown in the corss-sectional view in the figure. A rope wrapped around the the outer radius R1 = 1.0 m exerts a force of magnitude F1 = 5.0 N to the right. Asecond rope wrapped around another section of radius R2 = 0.50 m exerts a force of magnitude F2 = 6.0 N downward. The moment of inertia for a cylinder is 1/2MR^2. What is the angular acceleration of the cylinder? - 0.40 rad/s^2 - 0.60 rad/s^2 - 0.80 rad/s^2 - 1.0 rad/s^2
0.40 rad/s^2
A cylinder rotates wth constant angular acceleration about a fixed axis. The cylinder's motient of inertial about the axis is 4 kg m^2. 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. 0.5 rad/s^2 1 rad/s^2 2 rad/s^2 4 rad/s^2
0.5 rad/s^2
Which pair of mass and length gives the lowest moment of inertia for a uniform metal bad (moment of inertia equal to 1/3ml^2) spun around its end? - 0.0300 kg, 60 cm - 0.900 kg, 7.50 cm - 0.600 kg, 15.0 cm - 0.150 kg, 30.0 cm
0.900 kg, 7.50 cm
A rolling wheel of diameter of 68 cm slows down uniformly from 8.4 m/s to rest over a distance of 115 m. What is the magnitude of its angular acceleration if there was no slipping? - 0.91 rad/s^2 - 1.8 rad/s^2 - 5.7 rad/s^2 - 11 rad/s^2
0.91 rad/s^2
Mass m1 = 11 kg and mass m2 = 34 kg are balanced on a seesaw. The distance d1 + d2 between the two masses is 4.0 m. What is the distance d2? - 0.98 m - 1.3 m - 3.0 m - 12 m
0.98 m
A 375 g stone hangs from a thin light string that is wrapped around the circumference of a frictionless pulley with a moment of inertia of 0.0125 kgm^2 and a radius of 26 cm. When the stone is released, the stone accelerates downward and the pulley rotates about its axis as the string unwinds. What is the tension in the string? -0.0 N - 1.2 N - 2.4 N - 3.5 N
1.2 N
A string is wrapped tightly around a fixed pulley that has a moment of inertia of 0.0352 kgm^2 and a radius of 12.0 cm. A mass of 423 g is attached to the free end of the string. With the string vertical and taut, the mass is gently released so it can descend under the influence of gravity. As it descends, the string unwinds and causes the pulley to rotate but does not slip on the pulley. What is the speed of the mass after it has fallen through 1.25 m? - 1.97 m/s - 2.00 m/s - 2.28 m/s - 3.94 m/s
1.97 m/s
A solid uniform cylinder (I=1/2mr^2) is rolling without slipping. What fraction of its kinetic energy is rotational? - 1/3 - 2/3 - 1/2 - 1/4
1/3
The drive chain in a bicycle is applying a torque of 0.850 N • m to the wheel of the bicycle. You can treat the wheel as a thin uniform hoop (or ring) with a mass of 0.750 kg and a radius of 33.0 cm. What is the angular acceleration of the wheel? - 1.06 rad/s^2 - 3.43 rad/s^2 - 5.20 rad/s^2 - 10.4 rad/s^2
10.4 rad/s^2
A wheel rotates through an angle of 13.8 rad as it slows down uniformly from 22.0 rad/s to 13.5 rad/s. What is the magnitude of the angular acceleration of the wheel? - 0.616 rad/s^2 - 5.45 rad/s^2 - 10.9 rad/s^2 - 22.5 rad/s^2
10.9 rad/s^2
Initially, a small 2.0-kg rock is whirling at the end of a very thin string in a circular path of radius 0.75 m on a horizontal frictionless surface, as shown in the figure. The initial tangential speed of the rock was 5.0 m/s. The string has been slowly winding around a vertical rod, and a few seconds later the length of the string has shortened to 0.25 m. What is the instantaneous speed of the mass at the moment the string reaches a length of 0.25 m? - 3.9 m/s - 9.3 m/s - 15 m/s - 75 m/s
15 m/s
A uniform 3.0 m long ladder with mass of 6.0 kg rests on two sawhorses. Distance d1 is 0.90 m and d2 is 0.10 m. What is the magnitude of the force that the ladder exerts on sawhorse B?
18 N
A cylinder rotates with constant angular acceleration about a fixed axis. The cylinders moment of inertia about the axis is 4 kgm^2. At time t=0 the cylinder is at rest. At time t=2 seconds its angular velocity is 1 rad/s. What is the kinetic energy of the cylinder? - 1 J - 2 J - 3 J - 4 J
2 J
A solid sphere of mass m = 5.0 kg and radius r = 25 cm is rolling along a smooth floor with an angular velocity w = 3.1 rad/s. What is the total energy of the ball if the moment is equal to 2/5mr^2. - 0.60 J - 1.5 J - 2.1 J - 4.2 J
2.1 J
A solid sphere of mass m = 5.0 kg and radius r = 27 cm is rolling along a smooth floor with an angular velocity w = 7.9 rad/s. What is the linear velocity of the ball? - 2.1 m/s - 2.9 m/s - 3.7 m/s - 5.2 m/s
2.1 m/s
In a certain cyclotron, a proton of mass 1.67 × 10-27 kg moves in a circle of diameter 1.6 m with an angular speed of 2.0 × 106 rad/s. What is the angular momentum of the proton? - 1.3 x 10-21 kgm^2 - 1.8 x 10-21 kgm^2 - 2.1 x 10-21 kgm^2 - 3.2 x 10-21 kgm^2
2.1 x 10-21 kgm^2
A string is wrapped tightly around a fixed frictionless pulley that has a moment of inertia of 0.0352 kgm^2 and a radius of 12.5 cm. The string is pulled away from the pulley with a constant force of 5.00 N, causing the pulley to rotate. What is the speed of the string after it has unwound 1.25 m if the string does not slip on the pulley? - 1.18 m/s - 2.09 m/s - 2.36 m/s - 3.18 m/s
2.36 m/s
A uniform spool is suspended from a vertical wall by a string attached to the spool's thin axle. The axle is horizontal, as shown above. The wall is smooth so it exerts no frictional force on the spool. The tension in the string is 2.6 N. What is the weight of the spool? - 0.5 N - 1.0 N - 1.2 N - 2.4 N
2.4 N
As shown in the figure, a 3.53 kg box is attached to a light string that is wrapped around a cylindrical frictionless spool of radius 10.0 cm and moment of inertia 4.00 kgm^2. The spool is suspended from the ceiling and the box is then released from rest a distance 3.50 m above the floor. How long does it take the box to reach the floor? - 2.85 s - 2.97 s - 4.18 s - 5.89 s
2.97 s
At a certain instant, a compact disc is rotating at 210 rpm. What is its angular speed in rad/s? - 11 rad/s - 22 rad/s - 45 rad/s - 69 rad/s
22 rad/s
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 the axis perpendicular to the circle and through its center? - 9 kgm^2/s - 12 kgm^2/s - 18 kgm^2/s - 24 kgm^2/s
24 kgm^2/s
A system if two wheels fixed to each other is free to rotate about a frictionless axis through common center of the wheels and perpendicular to the page. Four forces exerted tangentially to the rims of the wheels, as shown above. The magnitude of the net torque on the system about the axis is - zero - FR - 2FR - 5FR
2FR
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? - 1.5 kg - 2.01 kg - 3.02 kg - 6.04 kg
3.02 kg
A 0.12 kg tetherball is attached to a pole by a 1.1 m long rope. If it circles the pole once in 2.0 s (and the rope is horizontal), how fast does it travel? - 1.7 m/s - 0.55 m/s - 1.1 m/s - 3.5 m/s
3.5 m/s
A solid uniform sphere (I=2/5mr^2) is rolling without slipping along a horizontal surface with a speed of 5.5 m/s when it starts up a ramp with an angle of 25 deg. with the horizontal. What is the speed of the sphere after it has rolled 3.0 m up as measured along the surface of the ramp? - 1.9 m/s - 2.2 m/s - 3.5 m/s - 4.0 m/s
3.5 m/s
A solid uniform disk (I = 1/2mr^2) of diameter 3.20 m and mass 42 kg rolls without slipping to the bottom of a hill, starting from rest. If the angular speed of the disk is 4.27 rad/s at the bottom, how high did it start on the hill? - 2.68 m - 3.14 m - 3.57 m - 4.28 m
3.57 m
A machinist turns the power on to a grinding wheel, at rest, at time t = 0 s. The wheel accelerates from rest for 10 s and reaches the operating angular speed of 38 rad/s. The wheel is run at that angular speed for 30 s and then power is shut off. The wheel slows down uniformly at 2.1 rad/s2 until the wheel stops. In this situation, what is the angular acceleration of the wheel between t=0.0 s and t=10.0 s? - 3.8 rad/s^2 - 4.6 rad/s^2 - 5.3 rad/s^2 - 5.3 rad/s^2
3.8 rad/s^2
A 350 g air track cart on a horizontal air track is attached to a string that goes over a frictionless pulley with a moment of inertia 6.00 x 10^-6 kgm^2 and a radius of 1.35 cm. The string is pulled vertically downward by a 255 g hanging mass. What is the magnitude of the acceleration of the cart? (picture)
3.92 m/s^2
A 95 N force exerted at the end of a 0.32 m long torque wrench produces a torque of 15 Nm. What is the angle between the wrench handle and the direction of the applied force? - 24 deg - 30 deg - 36 deg - 42 deg
30 deg
The lug nuts on a car wheel require tightening to a torque of 90 Nm. if a 30 cm long wrench is used, what is the magnitude of the minimum force required using the wrench? - 15 N - 30 N - 150 N - 300 N
300 N
A torque of 9.7 Nm is applied by twisting a screwdriver handle. How much force is applied tangentially to the screwdriver if the diameter of the handle is 5.3 cm? - 3.7 N - 5.1 N - 180 N - 360 N
360 N
a A horizontal, uniform board of weight 125 N and length 4 m is supported by vertical chains at each end. a person weighing 500 N is sitting on the board. the tension in the right chain is 250 N. what is the tension in the left chain? - 250 N - 375 N - 500 N - 625 N
375 N
A puck moves on a horizontal air table. It is attached to a string that passes through a hole in the center of the table. As the puck rotates about the hoel, the string is pulled downward very slowly and shortens the radius of rotation, so the puck gradually spirals towards the center. By what factor will the pucks angular speed have changed when the string's length has decreased to one-half of its original length? - 2 - 4 - radical2 - 1/2
4
Two uniform solid spheres with moment of inertia 2/5MR^2 have the same mass, but one has twice the radius of the other. The ratio of the larger sphere's moment of inertia about a central axis to that of the smaller sphere is - 1/2 - 4/5 - 2 - 4
4
A cylinder rotates with constant angular acceleration about a fixed axis. The cylinder's moment of inertia about the axis is 4 kgm2 . 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 = 2 seconds? - 1 kg^2 m/s - 2 kg^2 m/s - 3 kg^2 m/s - 4 kg^2 m/s
4 kg^2 m/s
A light-weight potter's wheel, having a moment of inertia of 24 kgm^2 is spinning freely at 40.0 rpm. The potter drops a small but dense clump of clay unto the wheel, where it sticks a distance 1.2 m from the rotational axis. If the subsequent angular speed of the wheel and clay is 32 rpm, what is the mass of the clay? - 2.8 kg - 3.7 kg - 4.2 kg - 4.6 kg
4.2 kg
A 1.53 kg bucket hangs on a rope wrapped around a pulley of mass 7.07 kg and radius 66 cm. this pulley is frictionless in its axle, and has the shape of a solid uniform disk (I1/2mr^2). After the bucket has been released, what is the angular acceleration of the pulley? - 2.6 rad/s^2 - 4.5 rad/s^2 - 9.8 rad/s^2 - 11 rad/s^2
4.5 rad/s^2
A hoop (I = mr^2) 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 deg below the horizontal. What is the rotational kinetic energy of the hoop after it has rolled down as measured along the surface of the ramp? 22 J 34 J 45 J 62 J
45 J
A solid uniform sphere ( I = 2/5mr^2) of mass 120 kg and radius 1.7 m starts from rest and rolls without slipping down an inclined plane of vertical height 5.3 m. What is the angular speed of the sphere at the bottom of the inclined plane? - 5.1 rad/s - 6.1 rad/s - 8.7 rad/s - 9.7 rad/s
5.1 rad/s
A solid uniform sphere (I 2/5mr^2) of mass 120 kg and radius 1.7 m starts from rest and rolls without slipping down an inclined plane of vertical height 5.3 m. What is the angular speed of the sphere at the bottom of the inclined plane? - 5.1 rad/s - 6.1 rad/s - 8.7 rad/s - 9.7 rad/s
5.1 rad/s
A solid uniform 3.33 kg (I = 1/2MR^2) has thin string of negligible mass wrapped around its rim, with one end of the string tied to the ceiling, as shown in the figure. The disk is released from rest, and as it falls, it turns as the string unwraps. At the instant it has fallen 2.25 m, how fast is the center moving? - 5.42 m/s - 6.53 m/s - 6.64 m/s - 29.4 m/s
5.42 m/s
An old 78 rpm record rotates through an angle of 320 deg. as it slows down uniformly from 78.0 rpm to 22.8 rpm. What is the magnitude of the angular acceleration of the record? - 2.34 rad/s^2 - 5.46 rad/s^2 - 6.50 rad/s^2 - 8.35 rad/s^2
5.46 rad/s^2
A 385 g tile hangs from one end of a string that goes over a pulley with a moment of inertia of 0.0125 kgm^2 and radius 15.0 cm. A mass 710 g hangs from the other end of the string. When the tiles are released, the larger one accelerates downward while the lighter one accelerates upward. The pulley has no friction in its axle and turns without the string slipping. What is the tension in the string on the side of the 710 g tile? - 3.68 N - 4.41 N - 5.59 N - 6.87 N
5.59 N
A machinist turns on the power on to a grinding wheel at time t= 0.0. The wheel accelerates uniformly from rest for 10.0 s and reaches the operating angular speed of 58 rad/s. The wheel is run at that angular velocity for 30.0 s, and then power is shut off. The wheel slows down uniformly at 1.4 rad/s^2 until the wheel stops. What is the approximate total number of revolutions made by the wheel in this situation? - 510 - 280 - 320 - 470
510
A figure skater rotating at 5.00 rad/s with arms extended has a moment of inertia of 2.25 kgm^2, If he pulls in his arms so his moment of inertia decreases to 1.80 kgm^2, what will be his new angular speed? - 0.81 rad/s - 2.25 rad/s - 4.6 rad/s - 6.25 rad/s
6.25 rad/s
A Ferris wheel rotating at 20 rad/s slows down with a constant angular acceleration of magnitude 5.0 rad/s2. How many revolutions does it make while slowing down before coming to rest? - 3.2 - 6.4 - 20 - 40
6.4
A torque of 12 Nm is applied to a solid, uniform disk (I=1/2mr^2) of radius 0.50 m. If the disk accelerates at 1.6 rad/s^2, what is the mass of the disk? - 15 kg - 30 kg - 45 kg - 60 kg
60 kg
A wheel accelerates from rest to 59 rad/s at a uniform rate of 58 rad/s^2. Through what angle (in radians) did the wheel turn while accelerating? - 24 rad - 30 rad - 38 rad - 60 rad
60 rad
A machinist turns the power on to a grinding wheel, which is at rest at time t = 0.00 s. The wheel accelerates uniformly for 10 s and reaches the operating angular speed of 96 rad/s. The wheel is run at that angular velocity for 50 s and then power is shut off. The wheel decelerates uniformly at 1.5 rad/s2 until the wheel stops. For how long a time after the power is shut off does it take the wheel to stop? - 62 s - 64 s - 66 s - 68 s
64 s
An ice skater has a moment of inertia of 5.0 kg m2 when her arms are outstretched, and at this time she is spinning at 3.0 rad/s. If she pulls in her arms and decreases her moment of inertia to 2.0 kg m2, how fast will she be spinning? - 2.0 rad/s - 3.3 rad/s - 7.5 rad/s - 10 rad/s
7.5 rad/s
A cinderblock of mass m=4.0 kg is hung from a nylon string that is wrapped around a frictionless pulley (I = 1/2 Mr^2), as shown in the figure. If the cinderblock accelerates downward at 4.90 m/s^2, what is the mass M of the pulley? - 2.0 kg - 4.0 kg - 6.0 kg - 8.0 kg
8.0 kg
A child riding a merry-go-round that has an instantaneous angular speed of 1.25 rad/s and an angular acceleration of 0.745 rad/s^2. The child is standing 4.65 m from the center of the merry-go-round. What is the magnitude of the linear acceleration of the child? - 3.46 m/s^2 - 4.10 m/s^2 - 7.27 m/s^2 - 8.06 m/s^2
8.06 m/s^2
What is the angular speed, in rad/s, of a flywheel turning at 813.0 rpm? - 85.14 rad/s - 13.53 rad/s - 63.84 rad/s - 95.33 rad/s
85.14 rad/s
A force of 30.0 N is applied to a wrench that is 0.31 meters long. What is the torque applied to the wrench? Assume the force acts perpendicular to the length of the wrench. - 9.3 Nm - 11 Nm - 30 Nm - 97 Nm
9.3 Nm
An old LP record that is originally rotating at 33.3 rad/s is given a uniform angular acceleration of 2.15 rad/s^2. Through what angle has the record turned when its angular speed reaches 72.0 rad/s? - 83.2 rad - 316 rad - 697 rad - 948 rad
948 rad
A scooter has wheels with a diameter of 120.0 mm. What is the angular speed of the wheels when the scooter is moving forward at 6.00 m/s. - 50.0 rpm - 72.0 rpm - 477 rpm - 955 rpm
955 rpm
When a fan is turned off, its angular speed decreases from 10 rad/s to 6.3 rad/s in 5.0 s. What is the magnitude of the average angular acceleration of the fan? - 0.37 rad/s^2 - 0.74 rad/s^2 - 0.86 rad/s^2 - 1.2 rad/s^2
?
A 5-kilogram sphere is connected to a 10-kilogram sphere by a rigid rod of negligible mass, as shown above. Which of the four lettered points represents the center of mass of the sphere-rod combination? - A - B - C - D
B
The figure above shows a uniform meter stick that is set on a fulcrum at its center. A force of magnitude F toward the bottom of the page is exerted on the meter stick at the position shown. At which of the labeled positions must be an upward force of magnitude 2F be exerted on the meter stick to keep the meter stick in equilibrium? - A - B - C - D
B
A solid disk whose plane is parallel to the ground spins with an initial angular speed W0. Three identical blocks are dropped onto the disk at locations A, B and C, one at a time, not necessarily in that order. Each block instantaneuoously sticks to the surface of the disk, slowing the disk's rotation. A graph of the angular speed of the disk as a function of time is shown. Based on the data presented in the graph, which of the following lists the points in the order in which the blocks are dropped onto the disk? - ABC - BCA - CAB - BAC
BAC
Consider a uniform hoop of radius R and mass M rolling without slipping. Which is larger, its translational kinetic energy or its rotational kinetic energy? - Translational kinetic energy is larger - Rotational kinetic energy is large - Both are equal - You need to know the speed of the hoop to tell
Both are equal
Which of the following statements correctly describes the forces and torques acting on an object in static equilibrium? - The net torque must be less than the net force - The net force be equal and opposite in value to the net torque - Both the net force and the net torque must be zero - Neither the net force nor the net torque can be zero
Both the net force and the net torque must be zero
Two objects, of masses 6.0 and 8.0 kilograms, are hung from the ends of a stick that is 70.0 centimeters and has marks every 10.0 centimeters, as shown. 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? (picture)
C
A disk of known radius and rotational inertia can rotate without friction in a horizontal plane around its fixed central axis. The disk has a cord of negligible mass wrapped around its edge. The disk is initially at rest, and the cord can be pulled to make the disk rotate. Which of the following procedures would best determine the relationship between applied torque and the resulting change in angular momentum of the disk? - Pulling on the cord, exerting a force of 15 N and then 35 N for 3 s and measuring the final angular velocity of the disk - For five different time intervals, pulling on the cord, exerting a force of 15 N, and then measuring the angle through which the disk rotates in each case. - For five different time intervals, pulling on the cord, exerting a force of 15 N, and then measuring final angular velocity of the disk. - For five forces of different magnitude, pulling on the cord for 5 s, and then measuring the final angular velocity of the disk.
For five forces of different magnitude, pulling on the cord for 5 s, and then measuring the final angular velocity of the disk.
Five forces act on a rod that is free to pivot at point P1 as shown in the figure. Which of these forces is produceing a counter-clockwise torque. about point P? - Force A - Force B - Force C - Force D
Force C
A disk with radius 0.5 m is free to rotate around its center without friction. A string is wrapped around the disk is pulled, as shown above, exerting a 2 N force tangent to the edge of the disk for 1 s. If the disk starts from rest, what is its angular speed after 1 s? - 4 rad/2 - It cannot be determined without knowing the rotational inertia of the disk - 1 rad/s - 0 rad/s
It cannot be determined without knowing the rotational inertia of the disk.
A platform is initially rotating on smooth ice with negligible friction, as shown at left in the figure. A stationary disk is dropped directly onto the center of the platform, a short time later, the disk and platform rotate together at the same angular velocity, as shown at the right in the figure. How does the angular momentum of only the platform change, if at all, after the platform drops? What is the justification for your answer? - It decreases. The top disk exerts a torque on the platform. - It decreases. The potential energy of the platform-disk-Earth system decreases when the disk drops. - It stays the same. Angular momentum is a conserved quantity. - It stays the same. The torques that the disk and platform exert on each other are equal in magnitude but in opposite directions.
It decreases. The top disk exerts a torque on the platform.
A system consists of a disk rotating on a frictionless axle and a piece of clay moving toward it, as shown in the figure above. The outside edge of the disk is moving at a linear speed v, and the clay is moving at sleep 1/2v. The clay sticks to the outside edge of the disk. How does the angular momentum of the system after the clay sticks compare to the angular momentum of the system before the clay sticks, and what is the explanation for the comparison? - It is the same because there is no external net torque on the system - it is greater because the rotating mass increases, which increases the rotational inertia - it is less because the speed of the disk decreases when the clay sticks to it - it is less because the angular momentum of the clay opposes that of the disk
It is the same because there is no external net torque on the system
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 amd hops onto one end, causing the board to slide and rotate. In this situation, which of the following occurs? - linear momentum is converted to angular momentum - rotational kinetic energy is conserved - translational kinetic energy is conserved - linear momentum and angular momentum are conserved
Linear momentum and angular momentum are 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. A force F is applied at the other end, at an angle theta 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? - Lsin0 - Lcos0 - L - Ltan0
Lsin0
Some bicycle brakes work by pressing rubber pads against the rim of the wheel. To test newly designed brakes, bicycle engineers mount a wheel of known rotational inertia on a low-friction axle, as shown above. The engineers spin the wheel with known initial angular speed and then apply the brakes with constant force. Which of the following procedures would enable th engineers to find the torque exerted by the brakes on the wheel? Select two answers - Measuring how much time the wheel takes to come to rest - Measuring how many rotations the wheel completes while coming to rest - Measuring the distance from axle to breaks and the normal force between the rubber pads and the rim - Measuring the mechanical energy dissipated as the rim rubs against the rubber pads.
Measuring how much time the wheel takes to come to rest and measuring how many rotations the wheel completes while coming to rest
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 - Mw^2R - MwR^2 1.2Mw^2R^2
MwR
The diagram above shows a top view of a child of mass M on a circular platform of mass 5M that is rotating counterclockwise. Assume the platform rotates without firction. Which of the following describes an action by the child that will result in an increase in the total angular momentum of the child-platform system? - The child moves toward the center of the platform. - The child moves away from the center of the platform. - The child moves along a circle concentric with the platform opposite the direction of the platform's rotation. - None of the actions describes will change the total angular momentum of the child-platform system.
None of the actions describes will change the total angular momentum of the child-platform system
Steel sphere A of mass M is moving along a horizontal surface with constant speed v. Identical see sphere B is at rest and hangs on a string of length R attached to a support at point P, as shown in the figure above. The spheres collide, and as a result sphere A stops and sphere B swings a vertical height h before coming momentarily to rest. Knowing values for which of the following will allow determination of the angular impulse on sphere B with respect to P due to the collision? - M and v only - M, v, and h - R and h - R, M, and v
R, M, and v
Two metal spheres are placed at the top of a wooden ramp. The spheres have identical masses and radii. Sphere 1 is hollow, with its mass all contained in a thin outer shell. Sphere 2, by contrast, is solid with its mass uniformly distributed throughout its volume. The two spheres are released at the same time and roll toward the bottom of the ramp. Which reaches the bottom first? - sphere 2 will reach the bottom first - neither sphere moves sphere 1 will reach the bottom first - the two will reach the bottom at the same time
Sphere 2 will reach the bottom first
Mars moves in an elliptical orbit around the Sun, and the mass of Mars is much less than the mass of the Sun. At the instant shown above, Mars is getting farther away from the Sun. How does this affect the potential energy of the Mars-Sun system and the magnitude of Mar's angular momentum with respect to the sun? - System U: Increases, Mars L: Increases - System U: Increases, Mars L: Remains the same - System U: Decreases, Mars L: Decreases -System U: Decreases, Mars L: Remains the same
System U: Increases, Mars L: Remains the same
A horizontal disk is free to rotate about an axle at its center. The labeled arrows in the figure represent forces of equal magnitude that are exerted on the edge of the disk in the directions shown. Which of the following correctly ranks the magnitude of T about the axle exerted by each force? - TA=TB=TC=TD - TA>TD>(TB=TC) - (TA=TB=TD)>TC - (TB=TC)>TD>TA
TA>TD>(TB=TC)
A disk and a hoop if the same mass and radius are released at the same time at the top of an inclined plane. If both are uniform, which one reaches the bottom of the inclined plane first if there is no slipping? - The hoop - The disk - Both each the bottom at the same time - It's impossible to tell
The disk
A merry-go-round spins freely when Diego moves quickly to the center along a radius of the merry-go-round. As he does this, it is true that - The moment of inertia of the system decreases and the angular speed increases - The moment of inertia of the system decreases and the angular speed decreases - The moment of inertia of the system increases and the angular speed increases - The moment of inertia of the system increases and the angular speed decreases
The moment of inertia of the system decreases and the angular speed increases
For this question of incomplete statement, two of the suggested answers will be correct. You must select both correct choices to earn credit. No partial credit will be earned if only one correct choice is selected. When a rigid object rotates about a fixed axis, what is true about all the points in the objects? - They all have the same angular speed - They all have the same tangential speed - They all have the same angular acceleration - They all have the same tangential acceleration - They all have the same radial acceleration
They all have the same angular speed and they all have the same angular acceleration
Consider a solid uniform sphere of radius R, mass M, and moment of inertia 2/5MR^2 rolling without slipping. Which form of its kinetic energy is larger, translational or rotational? - Translational kinetic energy is larger - Rotational kinetic energy is larger - Both are equal - You need to know the speed of the sphere to tell
Translational kinetic energy is larger
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 - g/5l - g/4l - 5g/7l
g/7l
A ball of mass m is attached to a vertical rod by two massless strings. The rod is rotated about its axis so that both strings are taught, with tensions T1 and T2 respectively. The string and rod form the right triangle shown in the figure above. The ball rotatexs in a horizontal circle of radius r with speed v. What is the tension T1 in the upper string? - mgcos0 - mgsin0 - mg/sin0 - mg/cos0
mg/cos0
Suppose a solid uniform sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on - the mass of the sphere - the radius of the sphere - both the mass and the radius of the sphere - neither the mass nor the radius of the sphere
neither the mas nor the radius of the sphere
A turntable that is initially at rest is set in motion with a constant angular acceleration alpha. What is the angular velocity of the turntable after it has made one complete revolution? - radical 2(alpha) - radical 2(pi)(alpha) - radical 4(pi)(alpha) - 2(alpha)
radical 4(pi)(alpha)
A sphere of mass M, radius r, and rotational inertia I is released from rest at the top of an inclined place of height h as shown above. If the plane has friction, what is the speed v of the center of mass of the sphere at the bottom of the incline? - radical(2gh) - (2Mghr^2)/I - radical((2Mghr^2)/I) - radical((2Mghr^2)/(I+Mr^2)
radical((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 place of height h as shown above. If the plane is frictionless, what is the speed v of the center of mass of the sphere at the bottom of the incline? - radical(2gh) - (2Mghr^2)/I - radical((2Mghr^2)/I) - radical((2Mghr^2)/(I+Mr^2)
radical(2gh)
The blocks are now dropped in the reverse order and the final angular speed of the disk is w2. How does w2 compare to w1. The final angular speed shown on the graph from the initial experiment? w2<w1 w2=w1 w2>w1
w2=w1
