Deck 8: Rotational Equilibrium and Rotational Dynamics

Question 1

Calculate the linear speed due to the Earth's rotation for a person at a point on its surface located at 70^o N latitude.The radius of the Earth is 6.40 × 10⁶ m.

A) 80 m/s
B) 465 m/s
C) 159 m/s
D) 437 m/s
E) ​573 m/s

Answer 1

159 m/s

Question 2

A bank vault is opened by applying a force of 100 N perpendicular to the plane of the door,1.1 m from the hinges.Find the torque due to this force about an axis through the hinges.

A) 91 N·m
B) 210 N·m
C) 100 N·m
D) 110 N·m
E) ​105 N·m

Answer 2

110 N·m

Question 3

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 20 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)
N
B)
N
C)
N
D)
N
E) ​
N

Answer 3

N

Question 4

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 5

A grindstone spinning at the rate of 18 rev/s has what approximate angular speed?

A) 57 rad/s
B) 5.7 rad/s
C) 36 rad/s
D) 113 rad/s
E) 28​ rad/s

Question 6

Tasha has mass 25 kg and wants to use a 5.0-m board of mass 12 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) 0.84 m
B) 0.42 m
C) 4.58 m
D) 4.16 m
E) ​1.62 m

Question 7

A ceiling fan is turned on and reaches an angular speed of 110 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) ​-0.3
B) -3
C) ​3
D) ​0.3
E) ​1.4

Question 8

A 0.300-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 4.00 rad/s,what is the tension in the string when the object is at the bottom of the circle?

A) 5.34 N
B) 12.54 N
C) 2.4 N
D) 11.76 N
E) ​10.68 N

Question 9

A 0.21-m radius grinding wheel takes 2.2 s to speed up from 4.0 rad/s to 13.0 rad/s.What is the wheel's average angular acceleration?

A) 8.2 rad/s²
B) 4.1 rad/s²
C) 1.4 rad/s²
D) 0.9 rad/s²
E) ​19.5 rad/s²

Question 10

A 4.0-m rod is pivoted about its left end.A force of 10 N is applied perpendicular to the rod at a distance of1.3 m from the pivot causing a ccw torque,and a force of 5.6 N is applied at the end of the rod 4.0 m from the pivot.The 5.6-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) 24.2 N·m
B) -1.8 N·m
C) 1.8 N·m
D) -24.2 N·m
E) ​-9.4 N·m

Question 11

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 0.70-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) 7.3 x 10⁷ ,2 rad/s
B)2.3 x 10⁸ ,0.2 rad/s
C) 3.5 x 10⁸ ,0.2 rad/s
D) 7.3 x 10⁷ ,0.2 rad/s
E) 2.3 x 10⁸ ,2​ rad/s

Question 12

A uniform bridge span weighs 80.0 × 10³ N and is 30.0 m long.An automobile weighing 12.0 × 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) 44.8 × 10³ N
B) 54 × 10³ N
C) 32.8 × 10³ N
D) 47.2 × 10³ N
E) 46 × 10³ N

Question 13

A uniform meterstick balances on a fulcrum placed at the 60-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) 0.6W
E) ​0.2W

Question 14

A 0.400-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) 18.32 N
B) 10.48 N
C) 14.4 N
D) 47.04 N
E) ​226.48 N

Question 15

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

A)

B)

C)

D)

Question 16

A spool of thread has an average radius of 1.00 cm.If the spool contains 142 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) 3,600
B) 4,500
C) 2,300
D) 1,100
E) ​23

Question 17

Two children seat themselves on a seesaw.The one on the left has a weight of 300 N while the one on the right weighs 200 N.The fulcrum is at the midpoint of the seesaw.If the child on the right is not at the end but is 2.00 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) -400 N·m
B) 400 N·m
C) 600 N·m
D) -600 N·m
E) ​200 N·m

Question 18

A bucket of water with total mass 23 kg is attached to a rope,which in turn,is wound around a 0.060-m radius cylinder at the top of a well.A crank with a turning radius of 0.5 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) 1878 N
B) 3 N
C) 27 N
D) 451 N
E) ​7 N

Question 19

1700 rev/min is equivalent to which of the following?

A) 3400 rad/s
B) 178 rad/s
C) 356 rad/s
D) 89 rad/s
E) ​28 rad/s

Question 20

A bucket filled with water has a mass of 24 kg and is attached to a rope,which in turn,is wound around a 0.070-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) 32 N·m
B) 16 N·m
C) 2 N·m
D) 343 N·m
E) ​235 N·m

Question 21

A 8.4-kg mass is placed at (4.0,5.0)m.Where can a 4.2-kg mass be placed so that the moment of inertia about the z axis is zero?

A) (−4.0,−5.0)m
B) (−8.0,−10)m
C) (−2.0,−2.5)m
D) (2.0,2.5)m
E) ​There is no position giving this result.

Question 22

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) 7.7 × 10−² kg·m²
B) 1.9 × 10−² kg·m²
C) 3.8 × 10−² kg·m²
D) 1.2 × 10−² kg·m²
E) 6.2 × 10−² kg·m²

Question 23

A uniform rod of length L and weight W is placed on a fulcrum a distance of 0.2L from the left end.On the left end is placed a mass of weight 3W 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)
W,up
B)
W,up
C)
W,down
D)
W,down
E) 0.6W,down

Question 24

An object consists of a rod (of length 4.0 m and negligible moment of inertia)to which five 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 60 kg·m².
B) is 20 kg·m².
C) is 32 kg·m².
D) is 8 kg·m².
E) ​cannot be uniquely determined until it is stated which inner mass the axis goes through.

Question 25

A 4.0-kg mass is placed at (2.0,3.0)m,and a 7.0-kg mass is placed at (2.0,−3.0)m.What is the moment of inertia of this system of masses about the y axis?

A) 143 kg·m²
B) 22 kg·m²
C) 99 kg·m²
D) 44 kg·m²
E) ​33 kg·m²

Question 26

A woman who weighs 500 N stands on an 8.0 m long board that weighs 200 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) 5.9 m
B) 3.1 m
C) 2.6 m
D) 2.1 m
E) ​4.9 m

Question 27

A meterstick is supported by a knife-edge at the 50-cm mark.Doug hangs masses of 0.40 and 0.80 kg from the 15-cm and 80-cm marks,respectively.Where should Doug hang a third mass of 0.20 kg to keep the stick balanced?

A) 100 cm
B) 10 cm
C) 90 cm
D) 0 cm
E) 50 cm

Question 28

A uniform,horizontal beam of length 8.0 m and weight 14 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) 8.1 N
B) 16.2 N
C) 97.0 N
D) 1.5 N
E) ​56.6 N

Question 29

A 300-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) 85°
B) 73°
C) 17°
D) 59°
E) ​9°

Question 30

Two hoops or rings (I = MR²)are centered,lying on a turntable.The smaller ring has radius = 0.05 m;the larger has radius = 0.1 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) 0.9 kg·m²
B) 0.135 kg·m²
C) 0.015 kg·m²
D) 0.075 kg·m²
E) ​0.06 kg·m²

Question 31

A bucket of water with total mass 25 kg is attached to a rope,which in turn is wound around a 0.04-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 5.0 m/s upon hitting the water surface in the well.What is the angular speed of the cylinder at this instant?

A) 50 rad/s
B) 31 rad/s
C) 125 rad/s
D) 157 rad/s
E) ​785 rad/s

Question 32

An 700-N billboard worker stands on a 5.0-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 780 N in that rope?

A) 1.2 m
B) 2.5 m
C) 1.85 m
D) 0.6 m
E) ​0.9 m

Question 33

A bowling ball has a mass of 9.0 kg,a moment of inertia of 3.6 × 10−² kg·m²,and a radius of 0.10 m.If it rolls down the lane without slipping at a linear speed of 3 m/s,what is its angular speed?

A) 90 rad/s
B) 30 rad/s
C) 27 rad/s
D) 0.030 rad/s
E) ​0.090 rad/s

Question 34

A 0.40-m radius automobile tire rotates how many rad after starting from rest and accelerating at a constant 2.0 rad/s² over a 6.0-s interval?

A) 14.4 rad
B) 30 rad
C) 36 rad
D) 72 rad
E) ​28.8 rad

Question 35

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 3
)Attached to the rod is a mass M at its midpoint and at the end opposite the pivot is another mass 3M.What is the moment of inertia of this configuration about the pivot?

A) 4

B) 3

C) 5

D) 6

E) ​None of the above answers is correct.

Question 36

A 3.0-kg mass is placed at (4.0,5.0)m,and a 6.0-kg mass is placed at (4.0,−5.0)m.What is the moment of inertia of this system of masses about the z axis?

A) 369 kg·m²
B) 36 kg·m²
C) 225 kg·m²
D) 144 kg·m²
E) ​45 kg·m²

Question 37

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 38

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) 0.036 kg·m²
B) 0.081 kg·m²
C) 0.041 kg·m²
D) 0.162 kg·m²
E) ​0.180 kg·m²

Question 39

A 3.0-kg mass is placed at (2.0,3.0)m,and a 6.0-kg mass is placed at (2.0,−3.0)m.What is the moment of inertia of this system of masses about the x axis?

A) 117 kg·m²
B) 18 kg·m²
C) 81 kg·m²
D) 36 kg·m²
E) ​27 kg·m²

Question 40

A majorette takes two batons and fastens them together in the middle at right angles to make an "x" shape.Each baton was 0.60 m long and each ball on the end is 0.10 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) 0.018 kg·m²
B) 0.036 kg·m²
C) 0.06 kg·m²
D) 0.12 kg·m²
E) ​0.054 kg·m²

Question 41

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)

Question 42

A ceiling fan is turned on and reaches an angular speed of 60 rev/min in 30 s.It is then turned off and coasts to a stop in 60 s.In the one minute of rotation,through how many revolutions did the fan turn?

A) 90
B) 180
C) 900
D) 120
E) ​240

Question 43

A 0.50-m radius automobile tire accelerates from rest at a constant 4.0 rad/s² over a 6.0 s interval.What is the tangential component of acceleration for a point on the outer edge of the tire during the 6.0-s interval?

A) 6.28 m/s²
B) 2 m/s²
C) 12.57 m/s²
D) 1.27 m/s²
E) ​4 m/s²

Question 44

A ventilation fan has blades 0.20 m in radius rotating at 30 rpm.What is the tangential speed of each blade tip?

A) 0.31 m/s
B) 0.20 m/s
C) 0.63 m/s
D) 37.70 m/s
E) ​6.00 m/s

Question 45

A baseball pitcher loosens up his pitching arm.He tosses a 0.15-kg ball using only the rotation of his forearm,0.26 m in length,to accelerate the ball.If the ball starts at rest and is released with a speed of 23 m/s in a time of 0.4 s,what torque is applied to the ball while being held by the pitcher's hand to produce the angular acceleration?

A) 33.2 N·m
B) 22.4 N·m
C) 2.2 N·m
D) 3.3 N·m
E) 221.2 N·m

Question 46

A Ferris wheel starts at rest and builds up to a final angular speed of 0.60 rad/s while rotating through an angular displacement of 2.5 rad.What is its average angular acceleration?

A) 0.09 rad/s²
B) 11.11 rad/s²
C) 0.15 rad/s²
D) 0.18 rad/s²
E) ​0.09 rad/s²

Question 47

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 23 m/s in a time of 0.4 s,what is the average angular acceleration of the arm and ball?

A) 2.9 rad/s²
B) 28.8 rad/s²
C) 18.4 rad/s²
D) 179.7 rad/s²
E) ​27.0 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 0.04 m.How many rev/s must the cylinder turn if the bucket is raised at a speed of 0.15 m/s?

A) 3.75 rev/s
B) 0.04 rev/s
C) 1.19 rev/s
D) 0.60 rev/s
E) ​2.39 rev/s

Question 49

A ventilation fan with a moment of inertia of 0.030 kg·m² has a net torque of 0.14 N·m applied to it.What angular acceleration does it experience?

A) 0.004 rad/s²
B) 4.7 rad/s²
C) 0.21 rad/s²
D) 0.3 rad/s²
E) ​0.17 rad/s²

Question 50

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 51

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 2.0 m rod with a mass of 3 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) 2.18 rad/s²
B) 2.25 rad/s²
C) 7.35 rad/s²
D) 1.63 rad/s²
E) ​4.90 rad/s²

Question 52

A Ferris wheel,rotating initially at an angular speed of 0.13 rad/s,accelerates over a 5.0-s interval at a rate of 0.050 rad/s².What is its angular speed after this 5.0-s interval?

A) 0.25 rad/s
B) 0.9 rad/s
C) 0.38 rad/s
D) 0.03 rad/s
E) ​0.19 rad/s

Question 53

An automobile accelerates from zero to 56 m/s in 7 s.The wheels have a diameter of 2 m.What is the average angular acceleration of each wheel?

A) 4 rad/s²
B) 8 rad/s²
C) 16 rad/s²
D) 48 rad/s²
E) ​6 rad/s²

Question 54

A bucket of water with total mass 29 kg is attached to a rope,which in turn is wound around a 0.04 m radius cylinder at the top of a well.A crank with a turning radius of 0.20 m is attached to the end of the cylinder and the moment of inertia of cylinder and crank is 0.11 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) 2.1 m/s²
B) 2.9 m/s²
C) 9.8 m/s²
D) 7.7 m/s²
E) ​6.9 m/s²

Question 55

A fan blade,initially at rest,rotates with a constant acceleration of 0.016 rad/s².What is its angular speed at the instant it goes through an angular displacement of 10 rad?

A) 0.40 rad/s
B) 0.16 rad/s
C) 0.32 rad/s
D) 0.57 rad/s
E) 1.79 rad/s

Question 56

A 0.30-m radius automobile tire accelerates from rest at a constant 3 rad/s².What is the centripetal acceleration of a point on the outer edge of the tire after 5 s?

A) 5.7 m/s²
B) 67.5 m/s²
C) 6.8 m/s²
D) 4.5 m/s²
E) ​45.0 m/s²

Question 57

A 0.30-m radius grinding wheel starts at rest and develops an angular speed of 20 rad/s in 5 s.What is the average tangential acceleration of a point on the wheel's edge?

A) 6 m/s²
B) 1.2 m/s²
C) 66.7 m/s²
D) 2.4 m/s²
E) ​100 m/s²

Question 58

A fan blade,initially at rest,rotates with a constant acceleration of 0.020 rad/s².What is the time interval required for it to reach a 10-rad displacement after starting from rest?

A) 32 s
B) 22 s
C) 100 s
D) 0.2 s
E) 45 s

Question 59

A Ferris wheel,rotating initially at an angular speed of 0.50 rad/s,accelerates over a 8.0-s interval at a rate of 0.05 rad/s².What angular displacement does the Ferris wheel undergo in this 7.00-s interval?

A) 1.60 rad
B) 4.20 rad
C) 5.60 rad
D) 7.20 rad
E) ​4.40 rad

Question 60

A disk has a moment of inertia of 2.8 × 10−⁴ kg·m² and rotates with an angular speed of 3.6 rad/sec.What net torque must be applied to bring it to rest within 3.9 s?

A) 3.9 × 10−⁴ N·m
B) 3.0 × 10−⁴ N·m
C) 5.0 × 10−⁴ N·m
D) 2.6 × 10−⁴ N·m
E) ​1.4 × 10−⁴ N·m