PRINCIPLES OF PHYSICS

Circular Motion

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)

r

Rotational Speed (scalar quantity)•number of times around the circle per unit time (rot/s)

Linear Speed (v)•Distance per unit time

smrrot

r

s

rot/2

1

21

Rotational Speed vs Linear Speed

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?

smsm

rot

m

s

rot/157/50

1

525

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

Centripetal Force

Changing Velocity

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 Force

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

Fc, acv

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.

Centripetal Force

We know: F = ma, so Fc = mac

ac = centripetal acceleration = v2/r

so, Fc = mac = mv2/r

Calculating Centripetal Force

Fc = mac ac = v2/r Fc = mv2/r

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 kgr = 0.5 mv = 6 m/s

ac = v2/r = (6m/s)2 /0.5 m = 72 m/s2

Fc = mac = 1 kg (72 m/s2) = 72 N

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 kgr = 20 mF = 400 N