Home Page of Peggy E. Schweiger

### Torque

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.

**Torque**in circular motion, the force
applied at a radial distance that changes the direction of motion of
a rotation; torque can stop, start, or change the direction of circular motion;
it is the "unbalanced force" of circular motion
t = F d
where t is the torque in Newton meters (
or N m), F is the perpendicular component of the applied force, and d is
the radial distance
When a torque is applied, rotation occurs around a **pivot point,
**or **fulcrum**

**Center of gravity**the point at which
the entire weight of an object seems to act
**Uniform**if an object is considered
uniform, its center of gravity is at its geometric center
**Rotational equilibrium**an object is
said to be in rotational equilibrium when all the torques acting on it are
balanced. A torque can cause a counterclockwise (cc) or a clockwise
rotation (cw).

St_{cw} =
St_{cc}
where S stands for "sum of"

### Rotational Motion

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.

**Angular displacement,q
**is the angle about the axis through which the object
turns. It is measured in degrees, revolutions, or the SI unit of radians.
1 revolution = 360° = 2
p radians
q = d/r
where d is the tangential distance
**Angular speed, w
**the rate at which an object rotates.
w = v/r
where v is the tangential velocity
**Angular acceleration, a
**the rate at which a rotating object changes angular speed
a = a/r
where a is the tangential acceleration

The equations for linear (tangential or translational) motion can be transformed into analogous rotational forms:

d = v t |
q = w t |

d = d_{o}+ v_{i} t + ½ at^{2} |
q = q
_{o} + w_{i} t + ½
a t^{2} |

v_{f} = v_{i} + at |
w_{f} = w
_{i} + a t |

v_{f}^{2} = v_{i}^{2} + 2 ad |
w_{f}^{2} =
w_{i}^{2} + 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.

t = F r
where r is the radius
Newton’s 2^{nd} law can be transformed into its analogous
rotational form:

**moment of inertia, I**the rotational
inertia of a rotating body. It is analogous to mass in translational
motion. The rotational inertia not only depends upon the rotating body's
mass, but also the distribution of that mass.
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/s^{2} |
a in rad/s^{2} |

force |
F in Newtons |
t in N m |

mass |
m in kg |
I in kg m^{2} |

Torque and Rotational Motion Sample Problems

Torque Homework

Rotational Motion Homework