Tangential and Centripetal Accelerations Physics Montwood High School.
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Transcript of Tangential and Centripetal Accelerations Physics Montwood High School.
Tangential and Centripetal Accelerations
PhysicsMontwood 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: in rad/srvT
Tangential and Angular Accelerations
• As the angular speed changes, so does vT. Therefore, as the angular acceleration changes, so does the tangential acceleration aT.
• Equation:
in rad/s2
raT
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 inUniform Circular Motion
ac
vTvTac
vT
acvT
ac2T
c
va
r
Centripetal Acceleration aC
• Centripetal acceleration is often called radial acceleration because it is directed along the radius toward the center of the circular path.
2C
2T
C
ra
rv
a
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
T
C1
T
C
2T
2Ctotal
2T
2C
2total
aa
tan
aa
tan
aaa
aaa
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.
N:unit
rmrvm
amF 22
TCC
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.