Centripetal Force

Equations:

Academic Vocabulary:

Þ Centripetal forceÞ Centripetal accelerationÞ Circular motionÞ Tangential velocityÞ Inverse square lawÞ Gravitational constantÞ Universal gravitational

forceÞ WeightlessnessÞ TorqueÞ Center of massÞ Lever armÞ Rotational Equilibrium

I CAN …

· explain the forces that cause circular motion· determine the motion of an object when the

centripetal force is removed.· differentiate between centripetal force, centripetal

acceleration and tangential velocity.· compare and contrast the directions of the centripetal

force, centripetal acceleration, and tangential velocity.

· calculate centripetal force and centripetal acceleration.

· compare universal gravitational force between objects with different distances using the inverse square law.

· calculate orbital velocity using centripetal force and universal gravitation equations.

· calculate torque from forces perpendicular to a lever arm.

· calculate the torque or force necessary for an object to be in rotational equilibrium.

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va tc

2

cc maF

221

r

mmGFG

rF

Inertia vs. ForceWhen a car accelerates, you feel as if you are flung backward.

Your inertia (mass) resists acceleration.

There is no force pushing you backward; your body wants to remain at rest as the car accelerates forward.

The Normal Force of the car seat pushes you forward, but your brain interprets this feeling as a force pushing you back into the seat.

Inertia vs. ForceWhen a car quickly stops, you feel as if you are flung forward.

Your inertia (mass) resists the negative acceleration.

There is no force pushing you forward; your body wants to remain in motion at constant velocity as the car accelerates backwards.

Your brain interprets the absence of the Normal Force of the car as a force pushing you forward. In reality, the only reason you do not fly through the windshield is because of the force of friction and normal force from the seatbelt pushing you backward.

Inertia vs. Force

When a car turns, you feel as if you are flung to the outside. Your inertia resists acceleration.There is no force pushing you to the outside of the turn; your body simply wants to keep moving in straight line motion!In every case, the REAL force is in the opposite direction of what your brain interprets.

The “Real” Force required to turn a car

1

2

3

• The car wants to continue its current motion.

• At location 1, the car wants to continue to move forward (up).

• The force required to make a turn (or circle) must be directed toward the center of the turn.

Uniform Circular Motion

2 Conditions:Uniform (constant) speedCircle has a constant radius.

Caused by a force

Centripetal Force: Force responsible for uniform circular motion.

Tangential velocity:Speed and direction of the object at any given time.

Fc

v Fc

Fc

v

Always toward center of circle!

v

Always tangent to the circle! (perpendicular to the Centripetal Force)

Centripetal Force•ALWAYS points toward the center of the circle.•NEVER changes an object’s speed. •ALWAYS changes the object’s direction.•ALWAYS perpendicular to the velocity.•If centripetal force is removed, the object will follow its tangential velocity.

Fc

v Fc

Fc

v

v

Concept Check:An object moves in a circular path with a constant speed.

a. Is the object’s velocity constant?No, direction of v is changing… but the

speed IS constant

b. Is its Fc constant?

No, direction of Fc is changing… but the magnitude of Fc is constant

Concept Check

Cause of Centripetal Force

Centripetal force is not a new type of force.You can always identify the real force which is causing the centripetal acceleration.Nearly any kind of force can act as a centripetal force.

Friction as Fc

As a car makes a turn, the force of friction acting upon the turned wheels of the car provide the centripetal force required for circular motion.

Tension as Fc

As a bucket of water is tied to a string and spun in a circle, the force of tension acting upon the bucket provides the centripetal force required for circular motion.

Normal Force as Fc

Centripetal force on a spinning carnival ride is from the normal force of wall or seat on you.

Gravity as Fc

As the moon orbits the Earth, the force of gravity acting upon the moon provides the centripetal force required for circular motion.

Combination of Forces as Fc

Centripetal force on a roller coaster is from the normal force and gravity combined.

If a hobo steals your truck keys and does donuts in the Wal-Mart parking lot, what is the centripetal force?

The frictional force that exists between your tires and the ground while turning causes the truck to maintain the circular motion necessary to generate a donut.

Could the hobo do donuts in a hockey rink if he stole a zomboni?

No, without friction, there is no Centripetal Force

Centripetal Acceleration: Acceleration responsible for uniform circular motion.

v

ac

v acac

v

Centripetal Acceleration

ac: centripetal acceleration in m/s2

v: tangential speed in m/sr: radius in meters

r

va tC

2

Centripetal ForceFc = m ac

Fc: centripetal force in N

vt: tangential speed in m/s

r: radius in meters

r

vmF t

C

2

Example 1A 0.5 kg object moves in a circular path with a radius of 0.25 m at a constant speed of 4.0 m/s. What is the magnitude of the object’s acceleration?

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2

ms

maC 25.0

)0.4( 2

ms

maC 25.0

16 2

2

264s

maC

Example 2A 5 kg bucket of water is being swung in a horizontal circle at a constant speed of 2.0 m/s. If the force required to keep the bucket moving in a circle is 25 N, What is the radius of the circular motion?

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C

2

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mkgN

2)0.2()5(25

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