Torque and Rotational Equilibrium
AP Physics B Content Objectives for Torque
Torque and rotational statics
Students should understand the concept of torque, so they can:
Calculate the magnitude and direction of the torque associated with a given force.
Calculate the torque on a rigid object due to gravity.
Students should be able to analyze problems in statics, so they can:
State the conditions for translational and rotational equilibrium of a rigid object.
Apply these conditions in analyzing the equilibrium of a rigid object under the
combined influence of a number of coplanar forces applied at different locations
TORQUE
A torque is an action that causes objects to rotate.
A torque is required to rotate an object, just as a force is required to move an object in a
line.
Torque is created by force, but it also depends on where the force is applied and the point
about which the object rotates.
The lever arm is the perpendicular distance between the line of action of the force and
the center of rotation
Force and lever arm are not always perpendicular. When the force and lever arm are not
perpendicular, trigonometry is required to calculate the length of the lever arm.
The force applied is perpendicular to the surface of the object rotating. When this force is at
an angle θ with the plane of the object, the perpendicular force requires the use of the sine
function. Therefore, the equation for torque is:
If more than one torque acts on an object, the torques are combined to determine the net
torque. If the torques tend to make an object spin in the same direction (clockwise or
counterclockwise), they are added together.
If the torques tend to make the object spin in opposite
directions, the torques are subtracted.
The units of torque are force times distance, or newton-meters.
A torque of 1 N-m is created by a force of 1 newton acting with
a lever arm of 1 meter.
ROTATIONAL EQUILIBRIUM
When an object is in rotational equilibrium, the net torque applied to it is zero.
For example, if an object such as a see-saw is not rotating, you know the
torque on each side is balanced
Rotational equilibrium is often used to determine unknown forces.
Any object that is not moving is in rotational equilibrium and in
translational equilibrium.
When a system is in equilibrium, and forces are non-concurrent, follow these steps to solve:
1. Determine as many forces as you can that act in the diagram. This may involve
finding the weight of various masses, or using FNet = 0 to analyze unknown forces.
2. Choose a pivot where unknown and un-wanted forces are acting, to eliminate them
from any torque calculations.
3. Determine the distances away from the pivot for each remaining force, including the
center-of-gravity force for the beam.
4. For any forces not perpendicular to the length of the beam (or the distance away
from the pivot), use trig to find the perpendicular component for each force.