Torques and Angular Momentum
Studio Physics I
Part I-Basics of Torques
Just as was the case for force, torque is a vector and so one must take its direction into account
when applying Newton’s second law. Torques which act in opposite direction are assigned
opposite signs (+ or -) and work against one another. Torques which act in the same direction
are assigned the same sign (+ or -) and reinforce one another. Hence, we need to get good at
determining the direction of a torque.
Determining the direction of Torque using =I
To answer questions regarding direction, DO NOT USE + OR – unless you have clearly defined
what direction you mean when you say + or -. Instead, try to use words like
clockwise, counter clockwise, up, down, right, left, into the page or out of
the page.
1. What is the direction of the angular velocity of the disk shown
at the left? (the axis points out of the page)
2. Do all points on the disk have the same angular velocity? Do
all points on the disk have the same linear velocity?
3. What is the direction of the angular acceleration of this disk if
it is speeding up?
4. What would the direction be of the torque necessary to make
this disk spin in the direction shown with an increasing angular
speed?
5. What is the direction of the angular acceleration of this disk if
it is slowing down?
6. What would the direction be of the torque necessary to make
this disk spin in the direction shown with an decreasing
angular speed?
7. What is the direction of the angular velocity of the disk shown
at the left?
8. What is the direction of the angular acceleration of this disk if
it is speeding up?
9. What would the direction be of the torque necessary to make
this disk spin in the direction shown with an increasing angular
speed?
10. Consider the pulley shown at the right. There is a mass
attached to a rope which is wrapped around the pulley. If the
mass is let free to fall, what is the direction of the angular
velocity of the pulley? What is the direction of the angular
acceleration? What is the direction of the torque that the mass
and rope exert on the pulley?
 1999-2001 K. Cummings
 
Determining the direction of Torque using   r  F

Part II
To answer questions regarding direction, DO NOT USE + OR – unless you have clearly
defined what direction you mean when you say + or -. Instead, use words like up, down,
right, left, into the page or out of the page.
11. Use the right hand rule to state the direction of c ab for each case shown below. (Hint: the
answer to A is out of the page)
A)
B)
C)
D)
a
b
a
a
b
a
b
12. Use the right hand rule to state the direction of c ba for each case shown above. What is
the relationship between ba and ab?
13. Consider the pulley shown at the left There is a mass attached to a rope which is wrapped
around the pulley. If the mass is let free to fall, what is the direction of the tension in the string?
Draw a set of two arrows, one which represents the direction of the tension in the string and one
which represents the radius of the pulley. The direction of the radius is determined by drawing
an arrow from the center of the pulley to the point at which the force (tension in this case) is
applied. Use these two arrows and rF to determine the direction of the torque produced by
the tension. Compare your answer to your answer in question # 10 above.
Part III Angular Momentum of a Point Object
14. Suppose you have a stone of mass 200 grams tied to the end of a rope of length
R=0.5 m. The stone is twirled in a circle of as shown in the figure below. The
linear velocity of the stone at one instant is also shown. (But the object continues
 1999-2001 K. Cummings
b
to move in circle the next instant.) What is the magnitude and direction of the
  
stone’s angular momentum at this instant? Hint:   rxp for a point mass.
v
15. Suppose everything about the problem statement above stays the same, except
the rope breaks at the instant shown. Hence, the stone moves in a line rather than
a circle in the moments that follow the instant shown. What is the magnitude
and direction of the stone’s angular momentum at this instant?
16. Consider the stone tied to the end of the rope shown in question #14 above. The
rope is not broken and the stone is moving in a circle. The stone has a angular
momentum (right?). Does the stone have a linear momentum even though it is
moving in a circle? Explain (or justify) your answer.
17. Now suppose that the rope has broken and the stone is moving is straight line.
The stone has a linear momentum (right?). Does the stone also have an angular
momentum? Explain (or justify) your answer.
18. When we want to talk about the linear position of an object, we have to chose an
origin that we measure the position with respect to. (That is, we can not just say
“three meters away”, we have to say “three meters away” from where). What do
you have to chose to define an angular momentum for an object moving linearly?
Why don’t you have to make this choice when the object moves in circle?
 1999-2001 K. Cummings