Vectors & Geometry
What is the magnitude of the vector A = <3,4,0>
5
What is the expression for the force on a mass m in a gravitational field g?
F = mg
The mathematical form for work done by a force.
W = ∫ F • dl
What does a graph of velocity vs time look like if acceleration is constant?
linear
This quantity is conserved for an object if the net external force acting on it is zero.
Linear momentum
Vectors A and B are perpendicular if their dot product is equal to this.
zero
This law describes the elastic force exerted by a spring
Hooke's Law: F = -kx
What are the base S.I units of energy?
kg m2/s2
With constant acceleration, how does position change with time?
Quadratically
Two ice skaters push off of one another from rest. What is the total momentum after the push?
In spherical coordinates, what is the direction of the radial unit vector?
Radially outward.
This force is necessary to facilitate circular motion
Centripetal Force
4x
What type of motion results from a constant force which is perpendicular to velocity?
Uniform circular motion.
This quantity is conserved if no external torques act on the system
Angular Momentum
The magnitude of the cross product between vectors A and B
ABsin(θ)
The gravitational force between two objects depends in what way on the distance between the objects>
For a conservative force, what is the relationship between force (F) and potential energy (U)?
F = -▽ U (the gradient of the potential energy)
In the absence of air resistance, this launch angle will maximize the range of a projectile.
45 degrees
A ball hits a wall and rebounds at the same speed. Compared to stopping upon impact, is the impulse larger, smaller, or the same?
Larger
These vectors specify how space is oriented in a given coordinate system and may be combined linearly to form other vectors.
Basis Vectors
Why is gravity called a conservative force?
Work is path independent.
This alternate to Newtonian mechanics uses the difference between kinetic and potential energies to arrive at equations of motion
Lagrangian Mechanics
A ball is dropped inside a train moving at constant velocity. How does the path of the ball appear to an observer on the train versus an observer standing on the station platform outside the train?
On train: straight down
On platform: parabola
These two quantities are conserved in an elastic collision.
Linear momentum and kinetic energy.