• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Noninertial reference frame

Suppose we are on a windowless bus that travels parallel to the Earth's surface at a constant acceleration with respect to the Earth's surface. How can a passenger in the bus determine the acceleration of the bus?
We decided we could attach a mass to a string and attach the string to the ceiling. From inside the bus, it would look like this:
________________
....\
.....\
......\
.......\
........O

Ignore those dots. Theyre the only way I can space things over.
There are two forces acting on this mass: gravity and the tension of the string. From the Earth's referece frame, the mass is accelerating with the same acceleration as the bus, ie, horizontally. So the only force the causes the mass to accelerate is TsinA=ma where T is the tension is the string, A is the angle measured wrt the line perpendicular to the ceiling, and a is the acceleration of the bus (and ball). Also, TcosA-mg=0 since there is no acceleration in this direction. Dividing each by each yields a=gtanA.
From the reference frame of the bus, the mass is stationary. TsinA=0 and TcosA=mg. Dividing each by each yields 0=tanA or A=0. Does this spurious result come from the fact that the reference frames are noninertial with repsect to each other? How come the result is valid for one frame but not the other?
 

Claude Bile

Science Advisor
1,471
19
Yes, with respect to the bus, you cannot say that TsinA=0 because the bus is an accelerating frame of reference. You must include this acceleration in any calculations that you make.

The principle of invariance only applies to inertial (non accelerating) frames of reference.

Claude.
 

Related Threads for: Noninertial reference frame

  • Posted
Replies
2
Views
995
Replies
1
Views
2K
Replies
1
Views
724
Replies
12
Views
492
  • Posted
Replies
9
Views
6K
  • Posted
Replies
9
Views
5K
  • Posted
Replies
3
Views
876
  • Posted
Replies
1
Views
2K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top