newton’s 2nd law applied to circular motion

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Why do we study circular motions?

Circular motions are everywhere around us!!!

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Newton’s 2nd law applied to Circular Motion

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Why do we study circular motions?

Circular motions are everywhere around us!!!

How can we describe a circular motion?

What causes a circular motion?

Questions:

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Uniform circular motion

Constant speed, or, “constant magnitude” of velocity

Motion along a circle: “changing direction” of velocity

First, uniform circular motion

ice

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Does the velocity change in uniform circular motion? iClicker Quiz

(a) Yes

(b) No

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Acceleration is NOT zero!

Net force acting on the object is

NOT zero.

The “net” force in circular motion is

called “Centripetal force”.

Direction of velocity: changing

Yes, velocity changes

amFnet

Does the velocity change in uniform circular motion?

Centripetal force is simply a net force that gives rise to a

circular motion, NOT a new type of force.

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Acceleration

Magnitude:

Direction: toward center of circle

Uniform circular motion

Magnitude:

Direction: toward center of circle

Net force (“Centripetal force”) 2

netmv

Fr

netF

netF netF

Derivations of the above relations (see textbook)

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Example: Circular motion of a hanging ball

m=4.8 kg

2m 22 deg

Find the tension in the rope and the speed of the ball.

iClicker Quiz: What is the direction of acceleration when the ball is at the position in the figure?

(a) (b) (c)

(d) Out of plane (e) into plane

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Non-Uniform circular motion

Changing speed, or, changing magnitude of velocity

Motion along a circle: Changing direction of velocity

Example

Why do we study non-uniform

circular motion?

Some exciting motions

are non-uniform circular motions!

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Radial component of acceleration 2

r

va

r

Even for Non-Uniform circular motion,

Radial component of net force

2

r

vF m

r

Radial components follow the same relations

as uniform circular motions!

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iClicker Quiz

For the roller coaster, the magnitude of normal force at A is _______ mg.

(a) equal to (b) less than (c) greater than

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Example

A roller coaster of mass m=1000 kg is passing point A at 30 m/s. Find the magnitude of normal force.

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iClicker Quiz

For the roller coaster, the magnitude of normal force at B is _______ mg.

(a) equal to (b) less than (c) greater than

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Example

A roller coaster of mass m=1000 kg is passing point B. Find the maximum speed it can have without losing contact with the track.

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Example: A ball of mass 0.5 kg attached to a rope is rotating in a vertical plane. What is the minimum speed the ball should have at the top to prevent the rope from becoming loose?

iClicker Quiz: At the bottom, the tension is ____ mg

(a) equal to (b) less than (c) greater than (d) not enough information !!!

2m