Transcript Tangential and Centripetal Accelerations

Tangential and Centripetal
Accelerations
Physics
Montwood High School
Relationship Between Angular and
Linear Quantities
• Tangential speed (vT) – the instantaneous linear
speed at a point for a rotating object.
– Point A and B both have the same angular velocity w.
The tangential velocity at point A and B are not equal.
The tangential velocity at point A is larger than the
tangential velocity at point B.
– For every turn, point A and B both move 360° or 2·
rad, but they travel a different arc length s. Point A has
to travel a greater distance s, so it has to have a greater
tangential speed vT.
• Equation:
vT  r  w
w in rad/s
Tangential and Angular Accelerations
• As the angular speed w
changes, so does vT.
Therefore, as the
angular acceleration a
changes, so does the
tangential acceleration
aT.
• Equation:
aT  r  a
 a in rad/s2
Centripetal Acceleration aC
• Centripetal acceleration
aC is the acceleration
directed toward the
center of a circle.
• A force is needed to
change the speed and/or
direction of an object
traveling on a circular
path. This force is
called the centripetal
force FC.
Centripetal Acceleration
Vectors in
Uniform Circular Motion
vT
vT
ac
ac
vT
ac 
r
2
ac
vT
ac
vT
Centripetal Acceleration aC
2
aC
aC
vT

r
2
 rw
• Centripetal
acceleration is
often called radial
acceleration
because it is
directed along the
radius toward the
center of the
circular path.
Tangential and Centripetal Acceleration
• Tangential aT and
centripetal aC
acceleration are
perpendicular to each
other.
• Tangential acceleration
aT is a result of a
change in speed.
• Centripetal
acceleration aC is a
result of a change in
direction.
Tangential and Centripetal Acceleration
2
2
a total  a C  a T
2
2
a total  a C  a T
aC
tan  
aT
  tan
1
aC
aT
2
Centripetal Force
• Centripetal force is the force that maintains
circular motion.
• Inertia tends to maintain the tangential
component of motion and the force directed
toward the center of the circle counters the
inertia and maintains the circular motion.
FC  m  a C
unit : N
m  vT2

 m  r  w2
r
Centripetal Force
• When the centripetal force is removed, the
object does not continue to move in a circle.
The object will move in a straight line that
is tangent to the point at which the force
stopped.