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.