Question 1

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?

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 2

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?

Accepted Answer

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 3

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?

Accepted Answer

A)  4
 
B)  3
 
C)  5
 
D)  6
 
E)  ​None of the above answers is correct.

Question 4

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?

Accepted Answer

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

Question 5

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. )

Accepted Answer

A)  1878 N 
B)  3 N 
C)  27 N 
D)  451 N 
E)  ​7 N

Question 6

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?

Accepted Answer

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

Question 7

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?

Accepted Answer

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

Question 8

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?

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

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?

Accepted Answer

A)  5.9 m 
B)  3.1 m 
C)  2.6 m 
D)  2.1 m 
E)  ​4.9 m

Question 11

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?

Accepted Answer

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 12

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?

Accepted Answer

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 13

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:

Accepted Answer

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 14

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

Accepted Answer

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 15

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?

Accepted Answer

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 16

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?

Accepted Answer

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 17

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?

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

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?

Accepted Answer

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

Question 20

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.

Accepted Answer

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

Exam 8: Rotational Equilibrium and Rotational Dynamics

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

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

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 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 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?

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

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 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.