before we start: get used to the direction of vectors for rotations. tangential velocity centripetal...

Before we start: get used to the direction of vectors for rotations.

rv

Tangential velocity

ra

Centripetal acceleration

Trying to solve problems in a non-inertial frame?

amF

Inertial frames

AamAmF

Non-Inertial frames

One example is the “centrifugal force”.

Another way of solving the train problem: given q=30, the radius of the train’s trajectory, R, what is the speed of the train?

In the frame of reference of the train, there is a fictitious force on any object of mass m that aims opposite the acceleration:

gmamF

mg

Rmv /2

q

)/(tan 2 gRv

From here we get the train speed.

First we solve a simple problem. What is the angle of the liquid in the accelerated pail?

In the frame of reference of the pail, there is a fictitious force on any object of mass m that aims opposite the acceleration:

gmamF

mg

ma

q

ga /tan

The surface of the liquid will be normal to the “net force”

What is the shape of the surfaceof a spinning bucket of water?

The normal to the surface will be along the direction of the “net force” (quotes indicate in this non-inertial frame) :

mg

rm 2

q

ga /tan

g

rzz

20

22

g

r

dr

dz 2

)tan(

Coriolis: you are on top of a Marry-go-round and through a ball.

On the ground the velocity of the ball is constant

2' tvx

)sin(' ttvx

On the rotating frame the trajectory looks accelerated

For Dt 0

vdt

xda 2''

2

2

There is an additional funny acceleration that is proportional to the velocity:Coriolis acceleration

Coriolis: you are on top of a Marry-go-round and through a ball.

On the ground the velocity of the ball is constant

rVaa

'2'

On the rotating frame the trajectory looks accelerated

Coriolis Centrifugal

The Earth equator is hot:Air raises, so currents of airflow from poles to equator.

Which way do you prefer it?

Focault’s pendulum: a pendulum at the North pole would oscillate on a plane that would rotate with 24-hour period. What is the period for us?

Focault’s pendulum pivot: It allows for the plane of oscillation to rotate freely.

A blimp has a velocity of 8.2 m/s due west relative to the air. There is a wind blowing at 3.5 m/s due north. The speed of the balloon relative to the ground is:

A. 11.7 m/sB. 8.9 m/sC. 7.4 m/sD. 4.7 m/sE. Some other speed (specify)

A blimp has a velocity of 8.2 m/s due west relative to the air. There is a wind blowing at 3.5 m/s due north. The speed of the balloon relative to the ground is:

A. 11.7 m/sB. 8.9 m/sC. 7.4 m/sD. 4.7 m/sE. Some other speed (specify)

An elevator moves downward with an acceleration of 6.2 m/s2. A ball dropped from rest by a passenger will have what downward acceleration relative to the elevator?

A. 3.6 m/s2.B. 6.2 m/s2.C. 9.8 m/s2.D. 16.0 m/s2.E. Some other acceleration (specify)

An elevator moves downward with an acceleration of 6.2 m/s2. A ball dropped from rest by a passenger will have what downward acceleration relative to the elevator?

A. 3.6 m/s2.B. 6.2 m/s2.C. 9.8 m/s2.D. 16.0 m/s2.E. Some other acceleration (specify)

N9T.4

When you go over the crest of a hill in a roller coaster, a force appears to lift you up out of your seat. This is a fictitious force, true (T) or false (F)?

N9T.4

When you go over the crest of a hill in a roller coaster, a force appears to lift you up out of your seat. This is a fictitious force, true (T) or false (F)?

N9T.5

If your car is hit from behind, you are suddenly pressed back into the seat. The normal force that the seats exerts on you is a fictitious force, true (T) or false (F)?

N9T.5

If your car is hit from behind, you are suddenly pressed back into the seat. The normal force that the seats exerts on you is a fictitious force, true (T) or false (F)?

N9T.5

If your car is hit from behind, you are suddenly pressed back into the seat. The normal force that the seats exerts on you is a fictitious force, true (T) or false (F)?

N9T.6

You are pressed downward towards the floor as an elevator begins to move upward. The force pressing you down is fictitious, true (T) or false (F)?

N9T.6

You are pressed downward towards the floor as an elevator begins to move upward. The force pressing you down is fictitious, true (T) or false (F)?

N9T.7

A beetle (black dot on the top view shown at the right) sits on a rapidly rotating turntable. The table rotates faster and faster, and eventually the beetle loses its grip. What is the subsequent trajectory relative to the ground (assuming it cannot fly)?

N9T.7

A beetle (black dot on the top view shown at the right) sits on a rapidly rotating turntable. The table rotates faster and faster, and eventually the beetle loses its grip. What is the subsequent trajectory relative to the ground (assuming it cannot fly)?

N9T.8

When is an elevator a reasonably good inertial reference frame?

A. Never under any circumstances.B. Always, since it is attached to the surface of the earth.C. It is except when it is changing speed.D. Other conditions (describe).

N9T.8

When is an elevator a reasonably good inertial reference frame?

A. Never under any circumstances.B. Always, since it is attached to the surface of the earth.C. It is except when it is changing speed.D. Other conditions (describe).

N9T.9

Is a freely falling elevator an accurate inertial reference frame?

A. No, such a frame is accelerating toward the earth.B. It is not a real inertial frame, but we can treat it as one if we ignore the gravitational forces on objects inside.C. Yes.D. It depends (explain).

N9T.9

Is a freely falling elevator an accurate inertial reference frame?

A. No, such a frame is accelerating toward the earth.B. It is not a real inertial frame, but we can treat it as one if we ignore the gravitational forces on objects inside.C. Yes.D. It depends (explain).