Deck 12: Torque

Question 1

If two forces of equal magnitude act on an object that is hinged at a pivot,the force acting farther from the pivot must produce the greater torque about the pivot.

A) True
B) False
C) unable to decide without knowing the shape of the object

Answer 1

False

Question 2

What is the magnitude of the cross product of a vector of magnitude 2.00 m pointing east and a vector of magnitude 4.00 m pointing 30.0° west of north?

A) 6.93
B) -6.93
C) 4.00
D) -4.00
E) 8.00

Answer 2

6.93

Question 3

If the torque on an object adds up to zero

A) the forces on it also add up to zero.
B) the object is at rest.
C) the object cannot be turning.
D) the object could be accelerating linearly but it could not be turning.
E) the object could be both turning and accelerating linearly.

Answer 3

the object could be both turning and accelerating linearly.

Question 4

A solid sphere,solid cylinder,and a hollow pipe all have equal masses and radii and are of uniform density.If the three are released simultaneously at the top of an inclined plane and roll without slipping,which one will reach the bottom first?

A) solid sphere
B) hollow pipe
C) solid cylinder
D) They all reach the bottom at the same time.

Question 5

A ball is released from rest on a no-slip surface,as shown in the figure.After reaching its lowest point,the ball begins to rise again,this time on a frictionless surface as shown in the figure.When the ball reaches its maximum height on the frictionless surface,it is

A) at a greater height as when it was released.
B) at a lesser height as when it was released.
C) at the same height as when it was released.
D) It is impossible to tell without knowing the mass of the ball.
E) It is impossible to tell without knowing the radius of the ball.

Question 6

If two vectors point in opposite directions,their cross product must be zero.

Question 7

A heavy boy and a lightweight girl are balanced on a massless seesaw.If they both move forward so that they are one-half their original distance from the pivot point,what will happen to the seesaw? Assume that both people are small enough compared to the length of the seesaw to be thought of as point masses.

A) It is impossible to say without knowing the masses.
B) It is impossible to say without knowing the distances.
C) The side the boy is sitting on will tilt downward.
D) Nothing will happen; the seesaw will still be balanced.
E) The side the girl is sitting on will tilt downward.

Question 8

If an irregularly shaped object (such as a wrench)is dropped from rest in a classroom and feels no air resistance,it will

A) accelerate but will not spin.
B) accelerate and turn until its center of gravity reaches its lowest point.
C) accelerate and turn about its center of gravity with uniform angular speed.
D) accelerate and turn about its center of gravity with uniform angular acceleration.
E) accelerate and spin until its center of gravity reaches its highest point.

Question 9

A uniform disk,a uniform hoop,and a uniform solid sphere are released at the same time at the top of an inclined ramp.They all roll without slipping.In what order do they reach the bottom of the ramp?

A) disk, hoop, sphere
B) hoop, sphere, disk
C) sphere, disk, hoop
D) sphere, hoop, disk
E) hoop, disk, sphere

Question 10

If and
Are nonzero vectors for which
•
= 0,it must follow that

A) ×
= 0.
B) is parallel to
.
C) | ×
| = AB.
D) | ×
| = 1.

Question 11

If the magnitude of the cross product of two vectors is one-half the dot product of the same vectors,what is the angle between the two vectors?

Question 12

What is the vector product of = 2.00
+ 3)00
+ 1)00
And
= 1)00
- 3)00
- 2)00
?

A) -3.00 + 5.00
- 9.00

B) -5.00 + 2.00
- 6.00

C) -9.00 - 3.00
- 3.00

D) -4.00 + 3.00
- 1.00

E) 2.00 -9.00
- 2.00

Question 13

When you ride a bicycle,in what direction is the angular velocity of the wheels?

A) to your left
B) to your right
C) forwards
D) backwards
E) up

Question 14

The angular momentum of a system remains constant

A) when the total kinetic energy is constant.
B) when no net external force acts on the system.
C) when the linear momentum and the energy are constant.
D) when no torque acts on the system.
E) all the time since it is a conserved quantity.

Question 15

Consider a uniform solid sphere of radius R and mass M rolling without slipping.Which form of its kinetic energy is larger,translational or rotational?

A) Its translational kinetic energy is larger than its rotational kinetic energy.
B) Its rotational kinetic energy is larger than its translational kinetic energy.
C) Both forms of energy are equal.
D) You need to know the speed of the sphere to tell.

Question 16

A metal bar is hanging from a hook in the ceiling when it is suddenly struck by a ball that is moving horizontally (see figure).The ball is covered with glue,so it sticks to the bar.During this collision

A) the angular momentum of the system (ball and bar) is conserved about the hook because only gravity is acting on the system.
B) the angular momentum of the system (ball and bar) is not conserved because the hook exerts a force on the bar.
C) the angular momentum of the system (ball and bar) is conserved about the hook because neither the hook nor gravity exerts any torque on this system about the hook.
D) both the angular momentum of the system (ball and bar) and its kinetic energy are conserved.
E) both the linear momentum and the angular momentum of the system (ball and bar) are conserved.

Question 17

If two vectors are perpendicular to each other,their cross product must be zero.

Question 18

The two rotating systems shown in the figure differ only in that the two identical movable masses are positioned at different distances from the axis of rotation.If you release the hanging blocks simultaneously from rest,and if the ropes do not slip,which block lands first?

A) The block at the left lands first.
B) The block at the right lands first.
C) Both blocks land at the same time.

Question 19

A tire is rolling along a road,without slipping,with a velocity v.A piece of tape is attached to the tire.When the tape is opposite the road (at the top of the tire),its velocity with respect to the road is

A) 2v.
B) v.
C) 1.5v.
D) zero.
E) The velocity depends on the radius of the tire.

Question 20

As you are leaving a building,the door opens outward.If the hinges on the door are on your right,what is the direction of the angular velocity of the door as you open it?

A) up
B) down
C) to your left
D) to your right
E) forwards

Question 21

A torque of 12 N • m is applied to a solid,uniform disk of radius 0.50 m,causing the disk to accelerate at 5.7 rad/s².What is the mass of the disk?

A) 17 kg
B) 13 kg
C) 8.5 kg
D) 4.3 kg

Question 22

A very thin horizontal,2.00-m long,5.00-kg uniform beam that lies along the east-west direction is acted on by two forces. At the east end of the beam,a 200-N force pushes downward. At the west end of the beam,a 200-N force pushes upward. What is the angular acceleration of the beam?

A) 240 rad/s² north
B) 1.33 × 10² rad/s² north
C) zero
D) 240 rad/s² south
E) 1.33 × 10² rad/s² south

Question 23

A 1.10-kg wrench is acting on a nut trying to turn it. The length of the wrench lies directly to the east of the nut. A force 150.0 N acts on the wrench at a position 15.0 cm from the center of the nut in a direction 30.0° north of east. What is the magnitude of the torque about the center of the nut?

A) 22.5 N • m
B) 11.3 N • m
C) 19.5 N • m
D) 2250 N • m
E) 1949 N • m

Question 24

A thin cylindrical shell is released from rest and rolls without slipping down an inclined ramp that makes an angle of 30° with the horizontal.How long does it take it to travel the first 3.1 m?

A) 1.4 s
B) 1.1 s
C) 2.1 s
D) 1.6 s
E) 1.8 s

Question 25

If = -2
- 6
+ 2
And
= -2
-2
- 3
,which of the following numbers is closest to the magnitude of
×
?

A) 25
B) 21
C) 17
D) 13
E) 9

Question 26

A 95 N force exerted at the end of a 0.50 m long torque wrench gives rise to a torque of 15 N • m. What is the angle (assumed to be less than 90°)between the wrench handle and the direction of the applied force?

A) 18°
B) 14°
C) 22°
D) 25°

Question 27

What is the torque about the origin on a particle located at


= 3 m
+ 4 m
- 2 m
If a force
= 5 N
- 2 N
+ 3 N
Acts on the particle?

A) (8 +
- 26
) N • m
B) (8 - 19
- 26
) N • m
C) (8 + 2
+
) N • m
D) (16 - 19
- 26
) N • m
E) (8 - 2
+
) N • m

Question 28

In an experiment,a student brings up the rotational speed of a piece of laboratory apparatus to 30.0 rpm.She then allows the apparatus to slow down uniformly on its own,and counts 240 revolutions before the apparatus comes to a stop.The moment of inertia of the apparatus is known to be 0.0850 kg•m².What is the magnitude of the retarding torque on the apparatus?

A) 0.0425 N • m
B) 0.159 N • m
C) 0.0787 N • m
D) 0.000278 N • m
E) 0.0000136 N • m

Question 29

A lawn roller in the form of a uniform solid cylinder is being pulled horizontally by a horizontal force B applied to an axle through the center of the roller,as shown in the figure.The roller has radius 0.65 meters and mass 51 kg and rolls without slipping.What magnitude of the force B is required to give the center of mass of the roller an acceleration of 2.8 m/s²?

Question 30

A force = 3.00 N
- 2)00 N
Acts at a location
= 1)00 m
+ 2)00 m
On an object. What is the torque that this force applies about an axis through the origin perpendicular to the xy-plane?

A) -1.00 N • m
B) 7.00 N • m
C) -3.00 N • m
D) 5.00 N • m
E) -8.00 N • m

Question 31

A very thin uniform rod,2.40 m long and of weight 135 N,has a frictionless hinge at its lower end.It starts out vertically from rest and falls,pivoting about the hinge.Just as it has rotated through an angle of 55.0°,what is the downward acceleration of the end farthest from the hinge?

A) 5.02 m/s²
B) 8.03 m/s²
C) 9.80 m/s²
D) 12.0 m/s²
E) 19.6 m/s²

Question 32

If = -4
- 2
- 3
,what is
×
?

A) +3 - 4

B) +3 + 4

C) -3 + 4

D) +3 + 2
- 4

E) -3 - 2
+ 4

Question 33

A light triangular plate OAB is in a horizontal plane.Three forces,F₁ = 6.0 N,F₂ = 9.0 N,and
F₃ = 7.0 N,act on the plate,which is pivoted about a vertical axes through point O.In the figure,
₂ is perpendicular to OB.Consider the counterclockwise sense as positive.The sum of the torques about the vertical axis through point O,acting on the plate due to forces F₁,F₂,and F₃,is closest to

A) 4.1 N • m
B) 5.4 N • m
C) -4.1 N • m
D) -5.4 N • m
E) zero

Question 34

A string is wrapped around a pulley with a radius of 2.0 cm and no appreciable friction in its axle.The pulley is initially not turning.A constant force of 50 N is applied to the string,which does not slip,causing the pulley to rotate and the string to unwind.If the string unwinds 1.2 m in 4.9 s,what is the moment of inertia of the pulley?

A) 0.17 kg • m²
B) 17 kg • m²
C) 14 kg • m²
D) 0.20 kg • m²
E) 0.017 kg • m²

Question 35

A 72.0-kg person pushes on a small doorknob with a force of 5.00 N perpendicular to the surface of the door. The doorknob is located 0.800 m from axis of the frictionless hinges of the door. The door begins to rotate with an angular acceleration of 2.00 rad/s². What is the moment of inertia of the door about the hinges?

A) 4.28 kg • m²
B) 7.52 kg • m²
C) 1.88 kg • m²
D) 0.684 kg • m²
E) 2.74 kg • m²

Question 36

A solid uniform sphere of mass 1.85 kg and diameter 45.0 cm spins about an axle through its center.Starting with an angular velocity of 2.40 rev/s,it stops after turning through 18.2 rev with uniform acceleration.The net torque acting on this sphere as it is slowing down is closest to

A) 0.00593 N • m.
B) 0.0372 N • m.
C) 0.0466 N • m.
D) 0.0620 N • m.
E) 0.149 N • m.

Question 37

For the vectors shown in the figure,find the magnitude and direction of the vector product ×
,assuming that the quantities shown are accurate to two significant figures.

A) 16, directed into the plane
B) 16, directed out of the plane
C) 45, directed on the plane
D) 45, directed into the plane
E) 45, directed out of the plane

Question 38

A uniform solid cylindrical log begins rolling without slipping down a ramp that rises 28.0° above the horizontal.After it has rolled 4.20 m along the ramp,what is the magnitude of the linear acceleration of its center of mass?

A) 9.80 m/s²
B) 4.60 m/s²
C) 3.29 m/s²
D) 3.07 m/s²
E) 2.30 m/s²

Question 39

For the vectors shown in the figure,find the magnitude and direction of ×
,assuming that the quantities shown are accurate to two significant figures.

A) 26, directed into the plane
B) 26, directed out of the plane
C) 31, directed on the plane
D) 31, directed into the plane
E) 31, directed out of the plane

Question 40

The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left),or a distance r/2 from the axis of rotation (right).You release the hanging blocks simultaneously from rest,and call t_L the time taken by the block on the left and t_R the time taken by the block on the right to reach the bottom,respectively.The bar,pulley,and rope have negligible mass,the rope does not slip,and there is no friction in the axle of the pulley.Under these conditions

A) t_L = t_R.
B) t_L = t_R.
C) t_L = t_R.
D) t_L = 2t_R.
E) t_l = 4t_R.

Question 41

A 20.0-kg uniform plank is supported by the floor at one end and by a vertical rope at the other as shown in the figure.A 50.0-kg mass person stands on the plank a distance three-fourths of the length plank from the end on the floor.
(a)What is the tension in the rope?
(b)What is the magnitude of the force that the floor exerts on the plank?

Question 42

A uniform solid sphere of mass 1.5 kg and diameter 30.0 cm starts from rest and rolls without slipping down a 35° incline that is 7.0 m long.
(a)Calculate the linear speed of the center of the sphere when it reaches the bottom of the incline.
(b)Determine the angular speed of the sphere about its center at the bottom of the incline.
(c)Through what angle (in radians)does this sphere turn as it rolls down the incline?
(d)Does the linear speed in (a)depend on the radius or mass of the sphere? Does the angular speed in (b)depend on the radius or mass of the sphere?

Question 43

A 3.00-kg ball rests in a frictionless groove as shown in the figure.
(a)What is the magnitude of the force that the left side of the groove exerts on the ball?
(b)What is the magnitude of the force that the right side of the groove exerts on the ball?

Question 44

Two identical ladders are 3.0 m long and weigh 600 N each.They are connected by a hinge at the top and are held together by a horizontal rope,1.0 m above the smooth floor forming a symmetric "A" arrangement.The angle between the ladders is 60° and both ladders have their center of gravity at their midpoint.What is the tension in the rope?

A) 240 N
B) 300 N
C) 220 N
D) 260 N
E) 280 N

Question 45

A uniform solid 5.25-kg cylinder is released from rest and rolls without slipping down an inclined plane inclined at 18° to the horizontal.How fast is it moving after it has rolled 2.2 m down the plane?

A) 4.3 m/s
B) 5.2 m/s
C) 3.0 m/s
D) 3.7 m/s
E) 2.6 m/s

Question 46

A light board,10 m long,is supported by two sawhorses,one at one edge of the board and a second at the midpoint.A small 40-N weight is placed between the two sawhorses,3.0 m from the edge and 2.0 m from the center.What forces are exerted by the sawhorses on the board?

Question 47

A uniform solid disk of radius 1.60 m and mass 2.30 kg rolls without slipping to the bottom of an inclined plane.If the angular velocity of the disk is 5.35 rad/s at the bottom,what is the height of the inclined plane?

A) 5.61 m
B) 4.21 m
C) 4.94 m
D) 6.73 m

Question 48

A solid,uniform sphere of mass 2.0 kg and radius 1.7 m rolls from rest without slipping down an inclined plane of height 7.0 m.What is the angular velocity of the sphere at the bottom of the inclined plane?

A) 5.8 rad/s
B) 9.9 rad/s
C) 11 rad/s
D) 7.0 rad/s

Question 49

A uniform 300-kg beam,6.00 m long,is freely pivoted at P,as shown in the figure.The beam is supported in a horizontal position by a light strut,5.00 m long,which is freely pivoted at Q and is loosely pinned to the beam at R.A load of mass is suspended from the end of the beam at S.A maximum compression of 23,000 N in the strut is permitted,due to safety.The maximum mass M of the load is closest to

A) 789 kg.
B) 554 kg.
C) 1020 kg.
D) 1090 kg.
E) 1320 kg.

Question 50

A uniform solid sphere is rolling without slipping along a horizontal surface with a speed of 5.50 m/s when it starts up a ramp that makes an angle of 25.0° with the horizontal.What is the speed of the sphere after it has rolled 3.00 m up the ramp,measured along the surface of the ramp?

A) 4.01 m/s
B) 8.02 m/s
C) 1.91 m/s
D) 2.16 m/s
E) 3.53 m/s

Question 51

A 120-kg refrigerator,2.00 m tall and 85.0 cm wide,has its center of mass at its geometrical center.You are attempting to slide it along the floor by pushing horizontally on the side of the refrigerator.The coefficient of static friction between the floor and the refrigerator is 0.300.Depending on where you push,the refrigerator may start to tip over before it starts to slide along the floor.What is the highest distance above the floor that you can push the refrigerator so that it won't tip before it begins to slide?

A) 0.710 m
B) 1.00 m
C) 1.21 m
D) 1.42 m
E) 1.63 m

Question 52

A 30.0-kg child sits on one end of a long uniform beam having a mass of 20.0 kg,and a 40.0-kg child sits on the other end. The beam balances when a fulcrum is placed below the beam a distance 1.10 m from the 30.0-kg child. How long is the beam?

A) 2.12 m
B) 1.98 m
C) 1.93 m
D) 2.07 m
E) 2.20 m

Question 53

A 500-g particle is located at the point = 4m
+ 3m
- 2m
And is moving with a velocity
= 5 m/s
-2 ms
+ 4 m/s
)What is the angular momentum of this particle about the origin?

A) (24 - 6
- 8
) kg∙m²/s
B) (12 - 3
- 4
) kg∙m²/s
C) (8 + 14
- 13
) kg∙m²/s
D) (10 -
+ 2
) kg∙m²/s
E) (4 - 13
- 11.5
) kg∙m²/s

Question 54

A nonuniform,80.0-g,meterstick balances when the support is placed at the 51.0-cm mark.At what location on the meterstick should a 5.00-g tack be placed so that the stick will balance at the 50.0 cm mark?

A) 16.0 cm
B) 67.0 cm
C) 66.0 cm
D) 35.0 cm
E) 34.0 cm

Question 55

A uniform sign is supported against a wall at point P as shown in the figure.If the sign is a square 0.40 m on a side and its mass is 4.0 kg,what is the magnitude of the horizontal force that the wall at P experiences?

A) 20 N
B) 0.00 N
C) 7.8 N
D) 98 N

Question 56

A 5.0-m long,12-kg uniform ladder rests against a smooth vertical wall with the bottom of the ladder 3.0 m from the wall.The coefficient of static friction between the floor and the ladder is 0.28.What distance,measured along the ladder from the bottom,can a 60-kg person climb before the ladder starts to slip?

A) 4.0 m
B) 3.7 m
C) 1.7 m
D) 1.3 m
E) 3.3 m

Question 57

A uniform solid cylinder of radius R and a thin uniform spherical shell of radius R both roll without slipping. If both objects have the same mass and the same kinetic energy,what is the ratio of the linear speed of the cylinder to the linear speed of the spherical shell?

A) / 2
B) / 2
C)
D) 4 /
E) 4 / 3

Question 58

An 82.0 kg-diver stands at the edge of a light 5.00-m diving board,which is supported by two narrow pillars 1.60 m apart,as shown in the figure.Find the magnitude and direction of the force exerted on the diving board
(a)by pillar A.
(b)by pillar B.

Question 59

In the figure,the horizontal lower arm has a mass of 2.8 kg and its center of gravity is 12 cm from the elbow joint pivot.How much force F_M must the vertical extensor muscle in the upper arm exert on the lower arm to hold a 7.5 kg shot put?

A) 100 N
B) 500 N
C) 750 N
D) 1000 N
E) 1500 N

Question 60

A child is trying to stack two uniform wooden blocks,12 cm in length,so they will protrude as much as possible over the edge of a table,without tipping over,as shown in the figure.What is the maximum possible overhang distance d?

A) 5 cm
B) 6 cm
C) 7 cm
D) 8 cm
E) 9 cm

Question 61

A uniform 300-kg beam,6.00 m long,is freely pivoted at P,as shown in the figure.The beam is supported in a horizontal position by a light strut,5.00 m long,which is freely pivoted at Q and is loosely pinned to the beam at R.A load of mass is suspended from the end of the beam at S.A maximum compression of 23,000 N in the strut is permitted,due to safety.Under maximum load,find the magnitude of the x component of the force exerted on the beam by the pivot at P.

A) 13,800 N
B) 12,800 N
C) 11,200 N
D) 14,400 N
E) 16,000 N

Question 62

A 10.0-kg uniform ladder that is 2.50 m long is placed against a smooth vertical wall and reaches to a height of 2.10 m,as shown in the figure.The base of the ladder rests on a rough horizontal floor whose coefficient of static friction with the ladder is 0.800.An 80.0-kg bucket of concrete is suspended from the top rung of the ladder,right next to the wall,as shown in the figure.What is the magnitude of the friction force that the floor exerts on the ladder?

A) 538 N
B) 706 N
C) 1290 N
D) 833 N
E) 601 N

Question 63

A dump truck has a large cubical concrete block in its bed.The coefficients of friction between this block and the floor of the bed are µ_k = 0.450 and µ_s = 0.650.As the bed is slowly tilted above the horizontal,will the brick first begin to slide or will it first tip over?

A) It will first tip over.
B) It will first begin to slide.
C) It will tip over just as it begins to slide.
D) It is impossible to answer without knowing the mass of the block.
E) It is impossible to answer without knowing the dimensions of the block.

Question 64

In the figure,a 10.0-m long bar is attached by a frictionless hinge to a wall and held horizontal by a rope that makes an angle θ of 53° with the bar.The bar is uniform and weighs 39.9 N.How far from the hinge should a 10.0-kg mass be suspended for the tension T in the rope to be 125 N?

Question 65

In the figure,a uniform rectangular crate 0.40 m wide and 1.0 m tall rests on a horizontal surface.The crate weighs 930 N,and its center of gravity is at its geometric center.A horizontal force F is applied at a distance h above the floor.If h = 0.61 m,what minimum value of F is required to make the crate start to tip over? Static friction is large enough that the crate does not start to slide.

Question 66

A 20.0-kg uniform door has a width of 1.20 m and a height of 2.50 m.The door is mounted on a post by a pair of hinges,marked 1 and 2 in the figure,at the top and bottom of the door.An external force of 60.0 N,at an angle of 30.0° above the horizontal,is applied to the small doorknob,as shown in the figure.The doorknob is 1.00 m above the bottom of the door.
(a)Find the x component of the force that hinge 1 exerts on the door at the top.
(b)Find the SUM of the y components of the forces that hinges 1 and 2 together exert on the door.

Question 67

In the figure,a uniform ladder 12 meters long rests against a vertical frictionless wall.The ladder weighs 400 N and makes an angle θ of 79° with the floor.A man weighing 790 N climbs slowly up the ladder When he has climbed to a point that is 7.8 m from the base of the ladder,the ladder starts to slip.What is the coefficient of static friction between the floor and the ladder?

Question 68

A solid uniform brick is placed on a sheet of wood.When one end of the sheet is raised (see figure),you observe that the maximum that the angle θ can be without tipping over the brick is 49.6°.There is enough friction to prevent the brick from sliding.What is the width w of the brick?

A) 5.18 cm
B) 6.09 cm
C) 6.81 cm
D) 9.40 cm
E) 10.5 cm