Vectors
Given the components of a vector, the magnitude can be found by applying this theorem:
The Pythagorean theorem
If an object is moving at constant velocity, Newton's first law tells us this:
ΣF = 0
The rate of change of the angle for an object in uniform circular motion is called this:
Angular frequency (ω)
When we say "no air resistance", that often means that the only force acting on a flying projectile is this:
Gravity
Bob drives a car going v1 in the positive x direction, and throws a ball out the window in the same direction. If Bob sees the ball going away from him at v2, an observer on the side of the road sees the ball moving at:
v1+v2
Given an angle from the HORIZONTAL and a magnitude, the i^ component of a vector can be found with this function:
Cosine (of the angle, then times the magnitude)
An accelerating object has its mass halved and the force acting on it doubled. The acceleration will do this:
The square of the velocity divided by the radius gives us the magnitude of this:
Centripetal acceleration
Our 1-D kinematics equations can be applied to higher dimensional problems by splitting the motion into these:
Component vectors
If an object travels a curved path at a constant speed, the dot product of the velocity and acceleration will always be this:
Zero
The CROSS product of a vector pointing only in the +X direction with one pointing only in the +Y direction will be a vector pointing in this direction:
+Z
Because they are acting on different systems, two equal and opposite forces as described by Newton's third law do not do this:
Cancel out
If tangential acceleration is greater than 0 and radius is constant, centripetal acceleration is doing this:
Increasing in magnitude
If a bullet fired from a gun hits the ground at the same time as one dropped from the same height, we can infer it was fired at this angle from the horizontal:
0°
A woman in an elevator drops her briefcase, but it does not fall to the floor. The elevator is doing this:
Accelerating downward at 9.81m/s2 (freefall)
The DOT product of the two vectors
(6.022x1023 i^ + 0 j^ + 0 k^)
and
(0 i^ + 𝜋100 j^ + 0 k^)
is equal to this number:
Zero
Centrifugal force isn't really a force, and it is never experienced in one of these:
Inertial reference frame
A 1-kilogram object moving in a 4 meter radius circle with a constant tangential velocity of 2 meters per second will have this acting on it:
1 Newton (of centripetal force)
If a projectile has a constant velocity in the x-direction and we want to know how far it goes, we might want to solve the kinematic equation in the y-direction for this:
Time
The textbook has an equation for total flight time given initial velocity and angle, but you need no air resistance and this other assumption:
Flat ground
To find the COSINE of the angle between two vectors, take THIS type of product and then divide by the product of THESE.
Dot product and the magnitudes of the vectors.
A box sits still on a ramp. The x-components of the normal and friction forces are equal and opposite to each other, and the y-components are equal and opposite to this:
Two objects in uniform circular motion have a mass of m and 2m. Compared to the first object, the second object experiences this much centripetal acceleration:
The same (but the force is doubled for the second object)
During the flight of an object, the y-component of the velocity is zero at this point:
The highest point
Assuming no air resistance, the speed of a projectile will equal the magnitude of the initial velocity at these times:
At launch and at impact