Vectors & 2D Motion
What information is necessary to fully describe a vector?
Magnitude and direction
The SI unit of force, defined as the amount of net force required to accelerate a 1-kg mass at 1 m/s²
newton (N)
Linear momentum is defined as the product of these two physical quantities
Mass and velocity
The rotational counterpart to mass in translational motion, measuring an extended rigid body's resistance to angular acceleration
The first condition for a rigid body to remain in static translational equilibrium requires this vector sum to be zero
the net external force
The dot product of two non-zero vectors that are perpendicular to each other always equals this
Zero
A sketch used to isolate a system of interest, showing only the external forces acting upon that system
Free-body diagram
The impulse delivered by a net force acting on an object over a given time interval equals the change in the object's motion
Change in momentum
The turning or twisting effect caused by a force, calculated as the cross product of the position vector and the force vector
Torque
The second condition for static equilibrium requires that this rotational quantity sum to zero about any chosen pivot axis
the net external torque
In ideal projectile motion over level ground, this is the only non-zero component of acceleration throughout the flight
-g
The change of momentum of a system is equal to the net external force acting on the system
A collision in which total kinetic energy is conserved alongside total linear momentum
Elastic collision
For an object rolling without slipping along a flat surface, the point on the wheel instantaneously in contact with the surface has this linear velocity relative to the ground
Zero
In a uniform gravitational field near Earth's surface, the center of gravity of an object is completely identical to this point
the center of mass
In uniform circular motion, the acceleration vector constantly points in this direction
Radially inward
The difference between static and kinetic friction
Total linear momentum is strictly conserved only when a system meets these two conditions
Constant mass and zero net external force
If a solid disk and a hollow hoop of the same mass and outer radius are released from rest at the top of an incline, the solid disk reaches the bottom first because it has a smaller value of this property.
moment of inertia
When applying the second condition of static equilibrium to an object that is completely stationary, you are allowed to choose this specific location as your pivot point.
Any point
This vector operation between two vectors is anticommutative, meaning reversing the multiplication order reverses the direction of the resultant vector
The cross product
When an elevator accelerates upward, a bathroom scale indicates a reading greater than the passenger's actual gravitational weight because the scale directly measures this contact force
The normal force
The weighted average position of the mass of an extended system of particles, which moves as though the entire mass were concentrated there and subjected to all net external forces
Center of mass
When a spinning figure skater pulls their outstretched arms in close to their body, their rotational speed increases because this vector quantity remains constant in the absence of net external torque.
angular momentum
When calculating torques to set up equilibrium equations, this term refers to the perpendicular distance from the chosen pivot point to the line of action of the force
the lever arm