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Circular Motion. Principles of Physics. r. When an object moves in a circle its path is described by:   Radius (r) – distance from the center to the perimeter (meters) Circumference (C) – perimeter of circle (2πr) (meters)

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Circular motion

Circular Motion

Principles of Physics


Circular motion

r

When an object moves in a circle its path is described by:  

Radius (r) – distance from the center to the perimeter (meters)

Circumference (C) – perimeter of circle (2πr) (meters)

Period (T) – time to go around the circle once (seconds)


Rotational speed vs linear speed
Rotational Speed vs Linear Speed

Rotational Speed (scalar quantity)

  • number of times around the circle per unit time (rot/s)

    Linear Speed (v)

  • Distance per unit time


Rotational speed vs linear speed1
Rotational Speed vs Linear Speed

Example: An object is moving around a circle of radius 5m. It completes 5 rotations every second. How fast is it going?


Centripetal force
Centripetal Force

  • Assume linear speed (what the speedometer in your car would read) is not changing during motion in a circle

  • Speed is constant

  • Direction is changing

  • If velocity is changing then the object is accelerating

  • If the object is accelerating then an unbalanced force must be acting on it

Changing Velocity


Centripetal force1
Centripetal Force

Remember: Newton’s 1st Law → objects in motion stay in motion in straight lines unless a force is acting

So, A force must be acting on an object if it is travelling in along a circular path

Special name – centripetal force (Fc)

(centripetal = center seeking)

**No such thing at centrifugal or centrifical force


Centripetal force2
Centripetal Force

  • To move in circles the direction of the force is always changing, but always directed toward the center of the circular path.

v

  • Fc, ac


Centripetal force3
Centripetal Force

Centripetal force is another name for any force that causes an object to move in circles

Therefore, Any type of force can be a centripetal force

Example: friction keeps cars moving around circular ramps when entering or exiting the highway.


Calculating centripetal force
Calculating Centripetal Force

We know: F = ma, so Fc = mac

ac = centripetal acceleration = v2/r

so, Fc = mac = mv2/r

Fc = macac = v2/r Fc = mv2/r


Circular motion

Example 1: A 1.0 kg ball attached to a string 0.50 m long is swung in a circle. Its speed along the circular path is 6.0 m/s. What are ac and Fc?

m = 1 kg

r = 0.5 m

v = 6 m/s

ac = v2/r

= (6m/s)2 /0.5 m

= 72 m/s2

Fc = mac

= 1 kg (72 m/s2)

= 72 N


Circular motion

Example 2: Suppose a 5 kg object is being held in a circular path of radius 20 m with a force of 400 N. What is the speed of the object?

Fc = mv2

r

400 = 5v2

20

400(20) = 5v2

5 5

1600 = v2

v = 40 m/s

m = 5 kg

r = 20 m

F = 400 N