Presentation on theme: "Before we start: get used to the direction of vectors for rotations. Tangential velocity Centripetal acceleration."— Presentation transcript:
Before we start: get used to the direction of vectors for rotations. Tangential velocity Centripetal acceleration
Trying to solve problems in a non- inertial frame? Inertial frames Non-Inertial frames One example is the “centrifugal force”.
Another way of solving the train problem: given =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: 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: The surface of the liquid will be normal to the “net force”
What is the shape of the surface of 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) :
Coriolis: you are on top of a Marry-go-round and through a ball. On the ground the velocity of the ball is constant On the rotating frame the trajectory looks accelerated For t 0 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 On the rotating frame the trajectory looks accelerated Coriolis Centrifugal
The Earth equator is hot: Air raises, so currents of air flow from poles to equator.
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/s B. 8.9 m/s C. 7.4 m/s D. 4.7 m/s E. Some other speed (specify)
An elevator moves downward with an acceleration of 6.2 m/s 2. A ball dropped from rest by a passenger will have what downward acceleration relative to the elevator? A. 3.6 m/s 2. B. 6.2 m/s 2. C. 9.8 m/s 2. D. 16.0 m/s 2. E. Some other acceleration (specify)
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.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).