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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Principles of Physics
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 (scalar quantity)
Linear Speed (v)
Example: An object is moving around a circle of radius 5m. It completes 5 rotations every second. How fast is it going?
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 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.
We know: F = ma, so Fc = mac
ac = centripetal acceleration = v2/r
so, Fc = mac = mv2/r
Fc = macac = 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 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
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
400 = 5v2
400(20) = 5v2
1600 = v2
v = 40 m/s
m = 5 kg
r = 20 m
F = 400 N