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Rotational Dynamics
Rode, Kiana, Tiana, and Celina
Force changes the velocity of a point object. In other words: a
force that is exerted in a very specific way changes the angular
velocity of an extended object.
Extended object- an object that has a definite shape and size.
There is an inverse relationship present here since to get the most
effect from the least force, you exert the force as far from the axis
of rotation as possible.
The magnitude of the force (distance from axis rotation to point
where force is being exerted) and the direction of the force
determine the change in angular velocity.
Lever arm- the perpendicular distance from the
axis of rotation to the point where the force is
being exerted.
Example: the hinge of a door (axis of rotation) and
the doorknob (point where force is being exerted.
Perpendicular- a straight line at an angle of 90
degree to a given line, place, or surface.
If the force is perpendicular to the radius of rotation
then the lever arm is the distance from the axis (r).
If the force is not perpendicular, the perpendicular
component of the force must be found.
To find the lever arm: extend the line of force until it forms a right angle
with a line from the center of rotation.
The distance between the intersection and the axis is the lever arm.
Equation: L= r sin θ
r= distance from axis of rotation to point where force is exerted
Θ = angle between the force and the radius from the axis of
rotation to the point where the force is applied.
L= lever arm
Torque- measure of how effectively a force causes
Magnitude of torque is product of force and lever
Measured in newtons-meters (N*m)
Represented by the Greek letter tau: T
Equation: T= Fr sin θ
Find the torque for each object T= Fgr
Fg= weight or force of gravity
r= radius or distance from center
Unless the force or radius change, the
torques are equal and opposite, resulting in a
net force of zero.
If you exert a force on a point mass, it's acceleration will be inversely proportional to its mass.
The amount of mass is not the only factor that a determines how much torque is needed to
change angular velocity.
Location of mass is another important factor
Moment of inertia- the resistance to rotation.
Represented by the symbol: I.
Has units of mass times the square of the distance.
For a point object located at a distance, r, axis of rotation, the moment of inertia is given by the
following equation: I= mr^2
M= mass
r= object's distance from axis of rotation
Point object- object
idealized as too small to be
located at only one
The moment of inertia for
complex objects depends on
how objects are from the axis
of rotation.
"I" also depends on the
location of the rotational axis.
Angular acceleration is directly proportional to the net torque and
inversely proportional to the moment of inertia.
NSL for linear motion is expressed as : a= Fnet/m.
NSL for rotational motion is represented by the equation: a= Tnet/I
Angular acceleration of an object is equal to the net torque on the
object, divided by the moment of inertia.
The greater the moment of inertia, the more torque needed to
produce the same angular acceleration.
Changes in the amount of torque applied to an object, or changes in
the moment of inertia, rate of rotation.