Deck 8: Rotational Equilibrium and Rotational Dynamics: Part A

Question 1

The torque caused by a force F applied at a distance r from the axis of rotation,is given by τ = rF​sinθ,where θ is the angle between
And
)If the magnitudes r and F remain the same,what other angle θ' will produce the same torque as was produced at angle θ if θ was less than 90°?

A) θ' = ​90° - θ
B) θ' = ​90° + θ
C) θ' = ​180° - θ
D) None of the above.

Answer 1

θ' = ​180° - θ

Question 2

A bucket of water with total mass 23 kg is attached to a rope,which in turn,is wound around a 0.080-m radius cylinder at the top of a well.A crank with a turning radius of 0.25 m is attached to the end of the cylinder.What minimum force directed perpendicular to the crank handle is required to just raise the bucket? (Assume the rope's mass is negligible,that the cylinder turns on frictionless bearings,and that g = 9.8 m/s². )

A) 45 N
B) 68 N
C) 72 N
D) 135 N

Answer 2

72 N

Question 3

Which of the first units given below can be units for angular acceleration while the second units can be units for angular velocity?

A) rev/min²,m/s
B) deg/hour,rev/minute
C) rad/s²,deg/hour
D) rad/s,rad/s²

Answer 3

rad/s²,deg/hour

Question 4

A bank vault is opened by applying a force of 300 N perpendicular to the plane of the door,1.2 m from the hinges.Find the torque due to this force about an axis through the hinges.

A) 180 N·m
B) 240 N·m
C) 300 N·m
D) 360 N·m

Question 5

A grindstone spinning at the rate of 12 rev/s has what approximate angular speed?

A) 3.2 rad/s
B) 26 rad/s
C) 52 rad/s
D) 75 rad/s

Question 6

Calculate the linear speed due to the Earth's rotation for a person at a point on its surface located at 30^o N latitude.The radius of the Earth is 6.40 × 10⁶ m.

A) 299 m/s
B) 233 m/s
C) 403 m/s
D) 465 m/s

Question 7

A bucket filled with water has a mass of 23 kg and is attached to a rope,which in turn,is wound around a 0.080-m radius cylinder at the top of a well.What torque does the weight of water and bucket produce on the cylinder if the cylinder is not permitted to rotate? (g = 9.8 m/s²)

A) 34 N·m
B) 18 N·m
C) 11 N·m
D) 36 N·m

Question 8

A uniform meterstick balances on a fulcrum placed at the 40-cm mark when a weight W is placed at the 20-cm mark.What is the weight of the meterstick?

A) W
B) 2W
C) W/2
D) 0.4W

Question 9

Two children seat themselves on a seesaw.The one on the left has a weight of 400 N while the one on the right weighs 300 N.The fulcrum is at the midpoint of the seesaw.If the child on the right is not at the end but is 1.50 m from the fulcrum and the seesaw is balanced,what is the torque provided by the weight of the child on the left? (Take ccw as positive. )

A) 600 N·m
B) 450 N·m
C) -600 N·m
D) -450 N·m

Question 10

A 0.12-m radius grinding wheel takes 2.1 s to speed up from 2.0 rad/s to 11.0 rad/s.What is the wheel's average angular acceleration?

A) 9.6 rad/s²
B) 4.3 rad/s²
C) 1.6 rad/s²
D) 0.33 rad/s²

Question 11

A circular disk is rotating about a central axis with an angular velocity which is increasing at a constant rate.Point 1 on the disk is located at a distance
From the center of the disk and point 2 on the disk is located at a distance
From the center of the disk.If
,which of the following ratios is the largest? 1 and 2 refer to being at points 1 and 2 in the subscripts below,all values occurring at the same time.

A)

B)

C)

D) All the ratios are 1 so none is larger.

Question 12

Tasha has mass 20 kg and wants to use a 6.0-m board of mass 10 kg as a seesaw.Her friends are busy,so Tasha seesaws by herself by putting the support at the system's center of gravity when she sits on one end of the board.How far is she from the support point?

A) 2.0 m
B) 1.0 m
C) 0.67 m
D) 0.33 m

Question 13

A ceiling fan is turned on and reaches an angular speed of 120 rev/min in 20 s.It is then turned off and coasts to a stop in an additional 60 s.The ratio of the average angular acceleration for the first 20 s to that for the last 60 s is which of the following?

A) 3
B) -3
C) 0.3
D) -0.3

Question 14

A 3.0-m rod is pivoted about its left end.A force of 10 N is applied perpendicular to the rod at a distance of 1.2 m from the pivot causing a ccw torque,and a force of 5.2 N is applied at the end of the rod 3.0 m from the pivot.The 5.2-N force is at an angle of 30^o to the rod and causes a cw torque.What is the net torque about the pivot? (Take ccw as positive. )

A) 18 N·m
B) −18 N·m
C) 4.2 N·m
D) −4.2 N·m

Question 15

A 0.200-kg object is swung in a circular path and in a vertical plane on a 0.500-m length string.If the angular speed at the bottom is 8.00 rad/s,what is the tension in the string when the object is at the bottom of the circle?

A) 8.36 N
B) 10.5 N
C) 16.7 N
D) 6.40 N

Question 16

A uniform bridge span weighs 70.0 × 10³ N and is 40.0 m long.An automobile weighing 15.0 × 10³ N is parked with its center of gravity located 12.0 m from the right pier.What upward support force does the right pier provide?

A) 24.5 × 10³ N
B) 35.5 × 10³ N
C) 65.0 × 10³ N
D) 45.5 × 10³ N

Question 17

A 0.60-kg rock is swung in a circular path and in a vertical plane on a 0.25-m length string.At the top of the path,the angular speed is 12.0 rad/s.What is the tension in the string at that point?

A) 7.9 N
B) 16 N
C) 22 N
D) 6.5 N

Question 18

A spool of thread has an average radius of 1.00 cm.If the spool contains 126 m of thread,how many turns of thread are on the spool? "Average radius" allows us to not need to treat the layering of threads on lower layers.

A) 100
B) 1000
C) 2000
D) 62,800

Question 19

1300 rev/min is equivalent to which of the following?

A) 2600 rad/s
B) 136 rad/s
C) 273 rad/s
D) 60 rad/s

Question 20

Suppose a car has a 100,000 mile 10 year warranty on the wheels and axles of a car.How may turns will the wheels of 0.80-m diameter make if both the mileage and time warranties run out simultaneously and what will be the average angular velocities of the wheel? (Assume that a mile = 1.6 x 10³
M and that a year is 3.16 x 10⁷ S)

A) 2.0 x 10⁸ , 1.3 x 10⁹ rad/y
B) 6.4 x10⁷ ,13 rad/s
C) 2.0 x 10⁸ ,0.51 rad/s
D) 6.4 x 10⁷ ,1.3 rad/s

Question 21

A 8.4-kg mass is placed at (3.0,4.0)m.Where can a 4.2-kg mass be placed so that the moment of inertia about the z axis is zero?

A) (−3.0,−4.0)m
B) (−6.0,−8.0)m
C) (−1.5,−2.0)m
D) There is no position giving this result.

Question 22

A bowling ball has a mass of 7.0 kg,a moment of inertia of 2.8 × 10−² kg·m²,and a radius of 0.10 m.If it rolls down the lane without slipping at a linear speed of 5.0 m/s,what is its angular speed?

A) 0.80 rad/s
B) 50 rad/s
C) 0.050 rad/s
D) 40 rad/s

Question 23

An object consists of a rod (of length 3.0 m and negligible moment of inertia)to which four small 2.0-kg masses are attached,one at each end and one at each point on the rod 1.0 m from each end.(The masses are one meter apart. )The moment of inertia of this object about an axis perpendicular to the rod and through one of the end masses:

A) is 28 kg·m².
B) is 12 kg·m².
C) is 4 kg·m².
D) cannot be uniquely determined until it is stated which inner mass the axis goes through.

Question 24

A uniform rod of length L and weight W is placed on a fulcrum a distance of 0.4L from the left end.On the left end is placed a mass of weight 2W and on the right end a vertical force F is applied to keep the system in balance.What are the magnitude and direction of the force F?

A)

B)

C)

D)

Question 25

Two hoops or rings (I = MR²)are centered,lying on a turntable.The smaller ring has radius = 0.050 m;the larger has radius = 0.10 m.Both have a mass of 6.0 kg.What is the total moment of inertia as the turntable spins? Ignore the mass of the turntable.

A) 0.030 kg·m²
B) 0.0075 kg·m²
C) 0.038 kg·m²
D) 0.075 kg·m²

Question 26

An 80-kg man is one fourth of the way up a 10-m ladder that is resting against a smooth,frictionless wall.If the ladder has a mass of 30 kg and it makes an angle of 60° with the ground,find the force of friction of the ground on the foot of the ladder.

A) 7.8 × 10² N
B) 2.0 × 10² N
C) 50 N
D) 1.7 × 10² N

Question 27

A baseball pitcher loosens up his pitching arm.He tosses a 0.20-kg ball using only the rotation of his forearm,0.32 m in length,to accelerate the ball.What is the moment of inertia of the ball alone as it moves in a circular arc with a radius of 0.32 m?

A) 1.5 × 10−² kg·m²
B) 2.0 × 10−² kg·m²
C) 4.0 × 10−² kg·m²
D) 7.6 × 10−² kg·m²

Question 28

A uniform,horizontal beam of length 6.0 m and weight 140 N is attached at one end to a wall by a pin connection (so that it may rotate).A cable attached to the wall above the pin supports the opposite end.The cable makes an angle of 60° with the horizontal.What is the tension in the cable needed to maintain the beam in equilibrium?

A) 81 N
B) 69 N
C) 70 N
D) 140 N

Question 29

A 4.0-kg mass is placed at (3.0,4.0)m,and a 7.0-kg mass is placed at (3.0,−4.0)m.What is the moment of inertia of this system of masses about the x axis?

A) 275 kg·m²
B) 90 kg·m²
C) 176 kg·m²
D) 99 kg·m²

Question 30

A 100-N uniform ladder,8.0 m long,rests against a smooth vertical wall.The coefficient of static friction between ladder and floor is 0.30.What minimum angle can the ladder make with the floor before it slips?

A) 22°
B) 51°
C) 18°
D) 59°

Question 31

A bucket of water with total mass 23 kg is attached to a rope,which in turn is wound around a 0.050-m radius cylinder at the top of a well.The bucket is raised to the top of the well and released.The bucket is moving with a speed of 6.0 m/s upon hitting the water surface in the well.What is the angular speed of the cylinder at this instant?

A) 39 rad/s
B) 79 rad/s
C) 120 rad/s
D) 160 rad/s

Question 32

A woman who weighs 500 N stands on an 8.0 m long board that weighs 100 N.The board is supported at each end.The support force at the right end is 2 times the support force at the left end.How far from the right end is the woman standing?

A) 4.0 m
B) 2.4 m
C) 2.7 m
D) 1.6 m

Question 33

A majorette takes two batons and fastens them together in the middle at right angles to make an "x" shape.Each baton was 0.90 m long and each ball on the end is 0.20 kg.(Ignore the mass of the rods. )What is the moment of inertia if the arrangement is spun around an axis through the center perpendicular to both rods?

A) 0.064 kg·m²
B) 0.096 kg·m²
C) 0.075 kg·m²
D) 0.16 kg·m²

Question 34

A 4.0-kg mass is placed at (3.0,4.0)m,and a 7.0 kg-mass is placed at (3.0,−4.0)m.What is the moment of inertia of this system of masses about the z axis?

A) 275 kg·m²
B) 90 kg·m²
C) 250 kg·m²
D) 180 kg·m²

Question 35

A uniform rod of length L and mass M is pivoted about one end.Attached to the rod is a mass M at its midpoint and at the end opposite the pivot is another mass M.What is the moment of inertia of this configuration about the pivot?

A)

B)

C)

D)

Question 36

An 800-N billboard worker stands on a 4.0-m scaffold weighing 500 N and supported by vertical ropes at each end.How far would the worker stand from one of the supporting ropes to produce a tension of 770 N in that rope?

A) 1.4 m
B) 2.0 m
C) 2.5 m
D) 2.7 m

Question 37

A 4.0-kg mass is placed at (3.0,4.0)m,and a 7.0-kg mass is placed at (3.0,−4.0)m.What is the moment of inertia of this system of masses about the y axis?

A) 275 kg·m²
B) 90 kg·m²
C) 176 kg·m²
D) 99 kg·m²

Question 38

A meterstick is supported by a knife-edge at the 50-cm mark.Doug hangs masses of 0.40 and 0.60 kg from the 35-cm and 80-cm marks,respectively.Where should Doug hang a third mass of 0.30 kg to keep the stick balanced?

A) 20 cm
B) 70 cm
C) 30 cm
D) 10 cm

Question 39

A majorette takes two batons and fastens them together in the middle at right angles to make an "x" shape.Each baton was 0.90 m long and each ball on the end is 0.20 kg.(Ignore the mass of the rods. )What is the moment of inertia if the arrangement is spun around an axis formed by one of the batons?

A) 0.081 kg·m²
B) 0.064 kg·m²
C) 0.19 kg·m²
D) 0.32 kg·m²

Question 40

A non-uniform rod of length L and mass M is pivoted about one end.The moment of inertia of this rod about its pivoted end is
)Attached to the rod is a mass M at its midpoint and at the end opposite the pivot is another mass 2M.What is the moment of inertia of this configuration about the pivot?

A)

B)

C)

D) None of the above answers is correct.

Question 41

A bucket of water with total mass 30 kg is attached to a rope,which in turn is wound around a 0.050 m radius cylinder at the top of a well.A crank with a turning radius of 0.25 m is attached to the end of the cylinder and the moment of inertia of cylinder and crank is 0.12 kg×m².If the bucket is raised to the top of the well and released,what is the acceleration of the bucket as it falls toward the bottom of the well? (Assume rope's mass is negligible,that cylinder turns on frictionless bearings and that g = 9.8 m/s². )

A) 3.2 m/s²
B) 3.8 m/s²
C) 7.4 m/s²
D) 9.8 m/s²

Question 42

If a nonzero torque is applied to an object,that object will experience:

A) a constant angular speed.
B) an angular acceleration.
C) a constant moment of inertia.
D) an increasing moment of inertia.

Question 43

A 0.40-m radius automobile tire accelerates from rest at a constant 2.0 rad/s².What is the centripetal acceleration of a point on the outer edge of the tire after 5.0 s?

A) 4.0 m/s²
B) 40 m/s²
C) 44 m/s²
D) 400 m/s²

Question 44

An automobile accelerates from zero to 30 m/s in 6.0 s.The wheels have a diameter of 1.0 m.What is the average angular acceleration of each wheel?

A) 5.0 rad/s²
B) 10 rad/s²
C) 25 rad/s²
D) 40 rad/s²

Question 45

A fan blade,initially at rest,rotates with a constant acceleration of 0.025 rad/s².What is its angular speed at the instant it goes through an angular displacement of 10 rad?

A) 0.025 rad/s
B) 0.11 rad/s
C) 0.46 rad/s
D) 0.71 rad/s

Question 46

A Ferris wheel starts at rest and builds up to a final angular speed of 0.70 rad/s while rotating through an angular displacement of 2.5 rad.What is its average angular acceleration?

A) 0.098 rad/s²
B) 0.05 rad/s²
C) 1.8 rad/s²
D) 0.60 rad/s²

Question 47

A rod of length L is hinged at one end.The moment of inertia as the rod rotates around that hinge is ML²/3.Suppose a 2.50 m rod with a mass of 3.00 kg is hinged at one end and is held in a horizontal position.The rod is released as the free end is allowed to fall.What is the angular acceleration as it is released?

A) 3.70 rad/s²
B) 7.35 rad/s²
C) 5.88 rad/s²
D) 4.90 rad/s²

Question 48

A bucket in an old well is hoisted upward by a rope which winds up on a cylinder having a radius of 0.050 m.How many rev/s must the cylinder turn if the bucket is raised at a speed of 0.20 m/s?

A) 3.0 rev/s
B) 1.5 rev/s
C) 0.48 rev/s
D) 0.64 rev/s

Question 49

A ventilation fan has blades 0.25 m in radius rotating at 30 rpm.What is the tangential speed of each blade tip?

A) 0.02 m/s
B) 0.52 m/s
C) 0.79 m/s
D) 20 m/s

Question 50

A 0.30-m radius automobile tire rotates how many rad after starting from rest and accelerating at a constant 3.0 rad/s² over a 5.0-s interval?

A) 12 rad
B) 25 rad
C) 37 rad
D) 0.50 rad

Question 51

A ventilation fan with a moment of inertia of 0.034 kg·m² has a net torque of 0.14 N·m applied to it.What angular acceleration does it experience?

A) 5.3 rad/s²
B) 4.1 rad/s²
C) 3.2 rad/s²
D) 0.31 rad/s²

Question 52

A Ferris wheel,rotating initially at an angular speed of 0.500 rad/s,accelerates over a 7.00-s interval at a rate of 0.0500 rad/s².What angular displacement does the Ferris wheel undergo in this 7.00-s interval?

A) 4.48 rad
B) 2.50 rad
C) 4.73 rad
D) 0.500 rad

Question 53

A 0.20-m radius grinding wheel starts at rest and develops an angular speed of 12.0 rad/s in 4.0 s.What is the average tangential acceleration of a point on the wheel's edge?

A) 0.45 m/s²
B) 0.60 m/s²
C) 28 m/s²
D) 14 m/s²

Question 54

A disk has a moment of inertia of 3.0 × 10−⁴ kg·m² and rotates with an angular speed of 3.5 rad/sec.What net torque must be applied to bring it to rest within 3.7 s?

A) 4.6 × 10−⁴ N·m
B) 7.5 × 10−⁴ N·m
C) 3.5 × 10−⁴ N·m
D) 2.8 × 10−⁴ N·m

Question 55

A Ferris wheel,rotating initially at an angular speed of 0.16 rad/s,accelerates over a 7.0-s interval at a rate of 0.050 rad/s².What is its angular speed after this 7.0-s interval?

A) 0.46 rad/s
B) 0.85 rad/s
C) 0.51 rad/s
D) 1.2 rad/s

Question 56

A baseball pitcher,loosening up his arm before a game,tosses a 0.15-kg ball using only the rotation of his forearm,0.32 m in length,to accelerate the ball.If the ball starts at rest and is released with a speed of 24 m/s in a time of 0.40 s,what is the average angular acceleration of the arm and ball?

A) 0.067 rad/s²
B) 94 rad/s²
C) 15 rad/s²
D) 190 rad/s²

Question 57

A fan blade,initially at rest,rotates with a constant acceleration of 0.025 rad/s².What is the time interval required for it to reach a 10-rad displacement after starting from rest?

A) 28 s
B) 2.0 s
C) 56 s
D) 18 s

Question 58

A ceiling fan is turned on and reaches an angular speed of 60 rev/min in 20 s.It is then turned off and coasts to a stop in 40 s.In the one minute of rotation,through how many revolutions did the fan turn?

A) 30
B) 60
C) 0
D) 600

Question 59

A baseball pitcher loosens up his pitching arm.He tosses a 0.15-kg ball using only the rotation of his forearm,0.32 m in length,to accelerate the ball.If the ball starts at rest and is released with a speed of 24 m/s in a time of 0.40 s,what torque is applied to the ball while being held by the pitcher's hand to produce the angular acceleration?

A) 1.1 N·m
B) 11 N·m
C) 2.9 N·m
D) 1.4 N·m

Question 60

A 0.40-m radius automobile tire accelerates from rest at a constant 2.0 rad/s² over a 5.0 s interval.What is the tangential component of acceleration for a point on the outer edge of the tire during the 5.0-s interval?

A) 33 m/s²
B) 0.80 m/s²
C) 0.60 m/s²
D) 0.30 m/s²

Question 61

A solid sphere of radius R is placed on an incline that makes an angle
With the horizontal.The sphere rolls down the incline without slipping.What is its acceleration?

A)

B)

C)

D)