Circular Motion and Gravitation

The water spills out once upside down because gravity overcomes centripetal force.

The bucket empties immediately as there is no force acting on the water.

The water stays inside due to centripetal force acting on it.

The water rises up out of the bucket because of free body motion.

No change as gravity depends solely on mass & radius not rotation rate

They will experience less gravity due to decreased centripetal acceleration

Increase apparent weight due to stronger centrifugal effects

Decrease apparent weight since increasing spin reduces effective gravity

The planet in an elliptical orbit varies its velocity along its path while maintaining constant angular momentum whereas velocity remains constant in a circular orbit.

The planet in the circular orbit sporadically increases and decreases velocity due to uniform circular acceleration constants.

Both planets maintain constant velocities throughout their respective orbits due to their consistent average distances from their star.

The planet in an elliptical orbit has a constantly faster velocity due to increased energy within non-circular paths.

Total system momentum decreases due to internal forces canceling out

Total system momentum increases due to their muscles' action

Total system momentum changes unpredictably because it depends on individual skater masses

Total system momentum remains constant

Thermal energy to kinetic energy

Kinetic energy to potential energy and back

Chemical energy to thermal energy

Nuclear energy to electrical energy

Tesla frames of reference

Newtonian frames of reference

Galilean frames of reference

Einstein frames of reference

Slows down because conservation angular momentum keeps velocity same despite smaller radius

Steady pace maintained as height drop balances out with increase earth pulling

Speeds up due larger earth pull causing faster movement

Remains steady until atmospheric drag reduces velocity overtime

Force

Speed

Acceleration

Velocity

The net force is equal to the product of mass and centripetal acceleration ($Fc = m \cdot a$)

The net force is equal to the mass divided by the triple centripetal acceleration ($Fc = \frac{m}{3} \cdot a_c$)

The net force is equal to half the mass multiplied by centripetal acceleration ($Fc = \frac{m}{2} \cdot a_c$)

The net force is equal to twice the mass multiplied by centripetal acceleration ($Fc = 2m \cdot a_c$)

Altimeter

Scale

Spectrometer

Odometer