Torque and Newton’s Second Law
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.
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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?
COPYRIGHT K. Cummings 1999, 2000
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Determining the direction of Torque using   r  F
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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
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.
Applying Newton’s Second Law with Torques
Newton’s second law F=ma can be just as useful for analyzing rotational motion as it was for
translational motion. However, in analyzing rotational motion, it is the sum of the torques acting on the
object that determines what the angular acceleration on the object will be. In other words, F=ma
becomes  = . . For objects in equilibrium (that is, stationary, balanced objects) both F=0 and =0
14.
COPYRIGHT K. Cummings 1999, 2000
COPYRIGHT K. Cummings 1999, 2000
Part II-Designing and Building a Mobile
COPYRIGHT K. Cummings 1999, 2000
Part III Angular Momentum
A student is standing on a frictionless turntable that is free to rotate about a vertical axis through
the student's center of mass. The rotational inertia of the student and turntable, about the axis of
rotation, is I = 3.0 kg·m². The student and turntable are initially at rest. A second student throws
a ball of mass 4.0 kg at a speed of 4.0 m/s which the student on the turntable catches. When the
ball is caught, it is 0.5 m distant from the axis of rotation, as shown in the sketch.
1) Find the angular momentum of the ball about the axis of rotation of the turntable before the
ball is caught.
2) Find the angular velocity of the student plus turntable plus ball after the ball has been caught.
3) Find the kinetic energy of the ball before it is caught.
4) Find the kinetic energy of the student plus turntable plus ball after the ball has been caught.
COPYRIGHT K. Cummings 1999, 2000