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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).

Stcw = Stcc

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 = 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.

t = F r
where r is the radius

Newton’s 2nd law can be transformed into its analogous rotational form:

F = ma t = I a

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/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

Torque Homework

Rotational Motion Homework