Why is a door knob located as far as possible from the door hinge? When you want to push open a door, you apply a force. Where you apply the force and in what direction you push are also important.
When a torque is applied, rotation occurs around a pivot point, or fulcrum
where S stands for "sum of"
Rotational motion is the motion of an object around an axis. Up to this point, we have only studied motion in a straight line (translational motion). Now we will study motion about an axis, or rotational motion. Objects can move translationally or rotationally or both. They can be in translational equilibrium, but not in rotational equilibrium, and vice versa.
Children on a merry-go-round all have different linear speeds (measured in m/s) depending on how far they are from the axis of rotation. They all have the same rotational speed (in rev/sec or rad/sec) no matter where they are located.
The equations for linear (tangential or translational) motion can be transformed into analogous rotational forms:
|d = v t||q = w t|
|d = do+ vi t + ½ at2||q = q o + wi t + ½ a t2|
|vf = vi + at||wf = w i + a t|
|vf2 = vi2 + 2 ad||wf2 = wi2 + 2 aq|
Just as an unbalanced force is required to change the motion of an object in linear (translational) motion, a torque is required to change the motion of an object in rotation motional.
Newton’s 2nd law can be transformed into its analogous rotational form:
|F = ma||t = I a|
Until this point, our study of physics has been concerned with translational motion, or motion in the xy plane. The standard English alphabet supplies the variables for this motion. We use the Greek alphabet for variables to distinguish rotational motion from translation motion. The following table lists variables for translational motion and the analogous rotational variable with their SI variables.
|distance/displacement||d in m||q in rad|
|speed/velocity||v in m/s||w in rad/s|
|acceleration||a in m/s2||a in rad/s2|
|force||F in Newtons||t in N m|
|mass||m in kg||I in kg m2|
Torque and Rotational Motion Sample Problems
Rotational Motion Homework