C H A P T E R   5Dynamics of Uniform

Circular Motion

C H A P T E R   5Dynamics of Uniform

Circular Motion

5.1. Uniform Circular Motion

5.1. Uniform Circular Motion

Uniform circular motion is the motion of an object traveling at a constant (uniform) speed on a circular path.

5.1. Uniform Circular Motion

Uniform circular motion is the motion of an object traveling at a constant (uniform) speed on a circular path.

The motion of a model airplane flying at a constant speed on a horizontal circular path is an example of uniform circular motion.

Period and Speed

Period and Speed

The period T is the time required to travel once around the circle—that is, to make one complete revolution.

Period and Speed

The period T is the time required to travel once around the circle—that is, to make one complete revolution.

The speed v is the distance traveled (circumference of the circle = 2r) divided by the time T:

5.2. Centripetal Acceleration

5.2. Centripetal Acceleration

5.2. Centripetal Acceleration

The centripetal acceleration of an object moving with a speed v on a circular path of radius r has a magnitude ac

given by:

5.2. Centripetal Acceleration

The centripetal acceleration of an object moving with a speed v on a circular path of radius r has a magnitude ac

given by:

Direction: The centripetal acceleration vector always points toward the center of the circle and continually changes direction as the object moves.

Derivation

The effect of the radius r on the centripetal acceleration.

Find the centripetal acceleration at each turn for a speed of 34 m/s.

5.3. Centripetal ForceThe centripetal force is the net force required to keep an object of mass m, moving at a speed v, on a circular path of radius r, and it has a magnitude of

5.3. Centripetal Force The centripetal force is the net force required to keep an object of mass m, moving at a speed v, on a circular path of radius r, and it has a magnitude of

Direction: The centripetal force always points toward the center of the circle and continually changes direction as the object moves.

Model Airplane

Question: What is the centripetal force for the model airplane flying in the horizontal plane?

Model Airplane

Question: What is the centripetal force for the model airplane flying in the horizontal plane?

Model Airplane

Question: What is the centripetal force for the model airplane flying in the horizontal plane?

Answer: The tension in the guideline is the centripetal force, which pulls the plane inward.

Car on a Flat-Curve

Question: What is the centripetal force for a car moving along a cul-de-sac?

Car on a Flat-Curve

Question: What is the centripetal force for a car moving along a cul-de-sac?

Car on a Flat-Curve

Question: What is the centripetal force for a car moving along a cul-de-sac?

Answer: Static frictional force between the road and the tires.

Question:Why do airplanes make banked turn?

Question:Why do airplanes make banked turn?

Answer:

To generate the centripetal force required for the circular motion.