Torque and Rotation Notes

The Torque and Rotation Interactive is an adjustable-size file that displays nicely on smart phones, on tablets such as the iPad, on Chromebooks, and on laptops and desktops. The size of the Interactive can be scaled to fit the device that it is displayed on. The compatibility with smart phones, iPads, other tablets, and Chromebooks make it a perfect tool for use in a 1:1 classroom.

This Interactive is inviting of numerous explorations pertaining to torque and the resulting rotation of an object about its axis of rotation. Users can begin by selecting an object to explore. There are three options: a disk, a rectangle, and a barbell. The attributes of each are modifiable. These include the mass, the dimensions, and the distance from the axis of rotation to the center of mass. By modifiable some of these attributes, a variety of other object types can be investigated. By modifying the inner and outer radius of the disk, one can investigate the effect of torque upon a very thin hoop or a ring of varying thickness. And by modifying the dimensions of a rectangle, one can investigate the effect of torque upon a square or even a solid bar. An added feature is the ability to modify the location of the axis of rotation. The axis can even be located outside the object (a massless arm extends from the object to the axis of rotation location).

In addition to the ability to modify the attributes of the object, users also have control over the amount of force, the location where the force is applied, and the direction of the force.

In all cases, a tap on the Start button begins the simulation. The Replay button returns the simulation to its initial state prior to tapping Start and restores the values of all input parameters. The Reset button resets all parameters to the initial default values. A tap on the Pause button will toggle the simulation between a play and a pause state.

There are three basic display modes - Pictures, Graphs, and Info - that users can toggle between. The Picture display will display the object with its dimensions and mass. The rotational inertia (I) of the object is displayed as well. The picture (along with the I value) will update in real time as alterations in any object attribute are made. The Pictures display also includes a sketch of the object, the location of its axis of rotation, the force vector (with magnitude and direction) and the arm length are displayed. The calculated torque value is also displayed; its value is updated in real time as changes are made to the arm length and the magnitude and direction of the force. The Graphs display will display graphs of the five output parameters - angular displacement (θ), angular velocity (ω), angular acceleration (α), angular momentum (L), and rotational kinetic energy (K) - as a function of time. Students can clearly see how values of these quantities relate to time (constant, inverse, linear, quadratic, etc.). As the simulation rules in Graphs display mode, digital values of rotational inertia, angular displacement, angular velocity, angular acceleration, angular momentum, and rotational kinetic energy are displayed in the simulation window. The final display mode is Info. In Info mode, a wealth of information and rotational equations are given. Values of input parameters used to calculate the five output parameters are shown; values are updated as the simulation runs. Information about the assumptions of the model are also included in Info mode.

The entire interface is very intuitive and easy to manipulate. A wealth of questions can be explored with the model.

The Physics Classroom has prepared a student activity sheet for use with this simulation. Teachers are welcome to download and use it with their classes. View Student Activity Sheet.
 

We added numerous resources to our website since the 2022-23 school year (and beyond) on the topic of torque, rotational motion, and angular acceleration. Here are a few that might blend well with the use of this Interactive.

• The Calculator Pad:
  Our recently-revised Calculator Pad section has a complete collection of problems on all sorts of torque and rotation topics. There are 8 problem sets on the topic of Rotational Dynamics. Each successive problem set becomes progressively more difficult than the one before it and they would make great follow-ups to this Interactive.
  
  View Rotation and Torque at The Calculator Pad

 

• Concept Builders:
  There are several Concept Builders on torque and rotation topics. Many would be suitable either as a follow up or a preface to this Interactive. The following would be worth considering:
  
  Torque
  
  Balanced vs. Unbalanced Torques
  
  Linear and Angular Velocity
  
  Angular Acceleration