A ladybug sits at the outer edge of a merry-go-round, and a
gentleman bug sits halfway between her and the axis of
rotation. The merry-go-round makes a complete revolution
once each second. The gentleman bug’s angular speed is
(a) half the ladybug’s.
(b) the same as the ladybug’s.
(c) twice the ladybug’s.
(d) impossible to determine
PI
Vector direction of rotational quantities
If a body is rotating, its direction of motion is constantly changing
so cannot be represented by a single vector in the plane of rotation.
However, we can use a single vector to give the direction of a
rotational quantity (e.g angular velocity ,angular acceleration 
and angular displacement  ) using the following convention:
a) Curl the fingers of the right hand so that they
point in the direction in which the rotational
quantity is positive
b) With the thumb at right angles to the plane of
the fingers, it points in the vector direction of the
quantity.
Or A right-hand screw, when rotated in the
sense of the rotational quantity, will advance in
the direction of the vector
A wheel is rotating as shown on the right
and slowing down.
Given the vector directions
(out)
a)
b)
(in)
c)
I) Which best represents direction of the
angular velocity?
II) Which best represents the direction of
the angular acceleration?
d)
  

For the following vectors
 A , B , C and D , which are the correct
vector directions for A  B and C  D ?

C
x 
D (into page)

A

B
(a)
(a)
(b)
(b)
(c)
• (out of page)
(d)
x (into page)
(e) None of the above.
(c)
(d)
• (out of page)
(C)
(e) None of the above.
Rank the following in order of decreasing torque.
(ii)
(i)
Force
(iii)
(iv)
a) i>ii>iii>iv
d) iv>iii>i>ii
b) iii>iv>ii>i
e) iv>iii>ii>i
c) iii~iv>ii>i

For this wrench, with applied force F, which is the best answer
below for the torque?
r
F 
 
a)   F  r

 
b)   r  F

 
c)   r  F

d)   rF sin 
e) b) and d)
Which of the following is (are) correct expression(s) for the torque?
 
(a)   r  F

 

(b)   F  r


(c)   I
(d)


  r
(e) (a) and (c)
You are trying to open a door that is stuck by pulling on the
doorknob in a direction perpendicular to the door. If you instead tie
a rope to the doorknob and then pull with the same force and in the
same direction, is the torque you exert increased?
(a) yes
(b) no
Which of the following objects has the largest moment of inertia
about the point O ?
r/2
2m
O
r
O
#1
m
#2
a) #1
b) #2
c) the moment of inertia is the same for both
The moment of inertia of a body rotating about an axis P-P is
given by
Ip 
 mr
i i
2
 m r  m2r2  m3r3    
2
11
2
2
i
The following objects have the same mass and radius. Which has
the largest moment of inertia?
P
Solid disk
(a) Solid disk
(b) Hollow disk
(c) Solid sphere
(d) All the same
P
Hollow disk
P
Solid sphere
There is a correspondence between variables for translational and
rotational motion. Which are the missing variables “_” in the
expressions below?
(a) 
(b) T
transl’n
Force
K. En.
Work
Power


F  ma
(c) "
rotat’n

 
P  Fv

  _
K  21 mv 2 K 
 
W  Fs
(d) I
1
2
I _2

W   _

P  _
(e) J
A box, with its center-of-mass off-center as indicated by the
dot, is placed on an inclined plane. In which of the four
orientations shown, if any, does the box tip over?
A force F is applied to a dumbbell for a time interval )t, first as in
(I) and then as in (II). In which case does the dumbbell acquire the
greater energy?
F
F
(I)
a) (I)
b) (II)
c) no difference
d) The answer depends on the rotational
inertia of the dumbbell.
PI
(II)
A force F is applied to a dumbbell for a time interval )t, first as in
(I) and then as in (II). In which case does the dumbbell acquire the
greater center-of-mass speed?
F
F
(I)
a) (I)
b) (II)
c) no difference
d) The answer depends on the rotational
inertia of the dumbbell.
PI
(II)
Which of the following best represents the
FBD of the beam on the right?
T
T
a)
b)
m2
m1
Cy
m1 g
Cx
m2 g
Cx
m2 g
m1 g
Cy
T
c)
Cx
T
d)
Cy
m2 g
m1 g
e) None of the above
Cy
Cx
m1 g
m2 g
pin hinge
T
For the situation given
on the previous slide, the
FBD of the beam is
Q
m2 g
P
m1 g
torque reference
direction
Cx
Cy
Which of the forces Cx, Cy,m1g, m2g, T produce positive torques
about
I)
Point P?
II) Point Q?
Answer (a) for yes and (b) for no
For the situation given
on the previous slide, the
FBD of the beam is
shown on the right.
The beam is of length l
and the angle between
the beam and the
horizontal is 
T
Q

m2 g
P
m1 g
Cx
Cy
The torque produced by m1 about point P is
a)m1 gl
b)m1 g cosl
c)m1 g sinl
d ) zero
The torque produced by m1 about point Q is
a)m1 gl
b)m1 g cosl
c)m1 g sinl
d ) zero
t - torque reference
direction
What is the direction of the angular momentum about the points
P, Q, R for a billiard ball (looking down on the table)
  
Recall: L  r  p
P

v
Q
R
(a)
(b)
(c)
(d)
(e)
Zero
What is the direction of the angular momentum about the points
P, Q, R for a rotating bicycle wheel (as seen from the side)
  
Recall: L  r  p
P
Q
R
(a)
(b)
(c)
(d)
(e)
Zero
Which best represents the correct free body diagram for a roller
coaster car on a frictionless track?
v
a)

ma
b)
N
N
mg
mg
d)
c)
N
mg
e) none of the above
N
mg
A solid cylinder rolls without
slipping down an inclined plane
as sketched on the right
Which of the following best represents the free body diagram of
the cylinder?
a)
b)
d) None of the above
c)
M
A solid cylinder rolls without
slipping down the inclined plane
shown on the right
R
h
How can you calculate its velocity at the bottom?
(a) Use conservation of energy .


(b) Use dynamics:   I
(c) Either (a) or (b) .
(d) None of the above.


and F  ma

A solid cylinder rolls without
slipping down the inclined plane
shown on the right
M
R
h

If one uses conservation of energy to calculate the cylinder’s
velocity at the bottom, what is the correct equation?
(a) Mgh = ½ Mv2
(b) Mgh = ½ Mv2 + ½IT2
(c) Mgh = ½IT2
(d) Mgh = ½ Mv2 + ½IT2 + fk h/sin()
(e) None of the above.
A hollow sphere and a hollow cylinder of the same mass and
radius are released from rest at the same height on a ramp. The
thickness of the wall is the same for both. They roll without
slipping. Which one reaches the bottom of the ramp first?
Hint: Either draw a free-body diagram and determine the torque
about the point of contact, or use conservation of energy.
Cylinder
Sphere
(a) they both arrive at the same time
(b) the sphere arrives first
(c) the cylinder arrives first
(d) not enough information to tell.
Consider the mass-pulley system to the right.
The string is wrapped around the pulley, which
is free to rotate.
Which of the following best represents the free body
diagrams for the pulley and block?
a)
b)
e) none of the above
c)
d)
R
M
m
Consider the mass-pulley system to the right.
The string is wrapped around the pulley, which
is free to rotate.
R
M
m
Which of the following is the correct equation of motion for
the block? T is the tension in the string.
(a) mg - T = ma
(b) T - mg = ma
(c) T - mg = 0
(d) None of the above