Inertial and Non-Inertial Frames of Reference

# Inertial and Non-Inertial Frames of Reference

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## Inertial and Non-Inertial Frames of Reference

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1. Inertial and Non-Inertial Frames of Reference

2. 1. Inertial Frames of Reference Consider a person in a car observing a ball suspended from the mirror when the car moves at a constant velocity east: FBD: FT The ball appears AT REST to the person in the car V constant Fg F=0 FT=Fg

3. 1b) To an observer outside the car the ball appears to be moving forward at a constant velocity. FBD is unchanged! FT V constant V constant F=0 Fg FT=Fg Both frames of reference are INERTIAL as the law of inertia holds!

4. 2a) Case 2: The car puts on the brake to slow down. Observation: The ball swings forward by angle ! FBD from stationary frame: a FTsin FT a Fx=ma FTcos Fx=FTsin v Fg Fy=0 FTcos =Fg ● The law of inertia still holds!

5. Case 2b: From inside the car the ball appears to suddenly swing forward. This only makes sense if a fictitious force is added to balance the horizontal tension component! FBD : FTsin Fx=0 FTcos FTsin=Ffict FT Ffict Fy=0 Fg FTcos =Fg ●The law of inertia only holds if a fictitious force is added!

6. Inertial vs. Non-Inertial Frames of Reference Inertial Frame of reference is one in which the law of inertia holds. A non-inertial frame is one in which the law of inertia is NOT valid. A fictitious force must be introduced to make sure Newton’s first law holds!

7. Case 3: Rotation viewed from stationary frame Observation: Imagine a child holding a yo-yo on a merry-go-round. The yo-yo will swing outwards. FBD from stationary frame: FTsin FTcos ac FT ac Fg ●An external observer sees the horizontal tension component as providing the necessary centripetal force!

8. Case 3b: Rotating Frame An observer in the frame sees the yo-yo at equilibrium. They must introduce a fictitious centrifugal force that acts radially outward! FTsin FTcos FT “Centrifugal” fictitious force Fg ●This fictitious force is really due to inertia-the object wants to continue moving in a straight line!