The velocity a falling object has when, due to air resistance, its acceleration is reduced to zero. This is the maximum velocity a falling object subject to air resistance can achieve.

Arrows represent

Two-dimensional vectors

The length of the arrow represents

The magnitude

Magnitude

Tells “how much”

Rule 3.1 (Arrows)

Arrows represent two-dimensional vectors. The length of the arrow is the magnitude of the vector while the arrow points out the direction.

Formula used to calculate the arrow’s length (magnitude)

Magnitude =√(Xmiles)^2+(Ymiles)^2

Formula used to calculate direction

Tan (⦵) = opposite side ÷ adjacent side

Equation used to calculate the angle

⦵= tan^-1 (y/x)

Rule 3.2 (adding vectors)

When adding vectors graphically, take the tail of the second vector and place it at the head of the first vector. The vector that then completes the triangle by starting at the tail of the first and pointing to the head of the second represents the sum of the two vectors.

Two-dimensional motion

Motion that occurs in a plane

Two-dimensional motion

Motion that occurs in a plane

Equation used to calculate a vector’s magnitude

Magnitude of A =√Ax²+Ay²

Equation used to calculate the direction of a vector

⊖=tan⁻¹(Ay/Ax)

Equation used to calculate the y-component of vector A

Ay=A﹒sin(⊖)

Equation used to calculate the x-component of vector A

Ax=A x cos(⊖)

Expression of Newton's second law

∑F=ma

The Newton

The SI unit of force and weight (weight is a force) defined as kgm/sec^2

Dyne

Unit of force used for smaller objects and forces, defined as g x cm/sec^2

Weight equation

W=mg

Pound

English unit of force, defined as slug ft/sec^2

f=µFn, where f = magnitude of friction, Fn = the normal force, and µ = the coefficient of friction.

An equation for the Frictional Force

Friction

A force that opposes motion, resulting from the contact of two surfaces.

Newton's first law (The Law of Inertia)

An object in motion (or at rest) will tend to stay in motion (or at rest) until it is acted upon by an outside force.

Newton's Second Law

When an object is acted on by one or more outside forces, the vector sum of those forces is equal to the mass of the object times the resulting acceleration vector.

Normal Force

A force that results from the contact of two bodies and is perpendicular to the surface of contact.

Kinetic friction

Friction that opposes motion once the motion has already started.

Static friction

Friction that opposes the initiation of motion.

Sir Isaac Newton's date of birth

1642

Slug

Standard English unit for mass

Mass

A scalar quantity that measures matter

Weight

A vector quantity that measures the gravitational pull on an object

2 things that affect the strength of the frictional force between an object and a surface

(1) The nature of the object and the surface, and (2) the normal force that the surface exerts on the object.

Translational Equilibrium

An object is said to be in translational equilibrium when the sum of the forces acting on it is equal to zero.

Static equilibrium

When an object is at rest, it is said to be in static equilibrium.

Dynamic equilibrium

When an object moves with a constant velocity, it is said to be in dynamic equilibrium.

Tension

The force from a tight string, rope, or chain. This force is directed away from the object to which the string, rope, or chain is anchored.

Translational motion

Motion from one point to another which does not involve repeatedly passing the same point in space.

Rotational motion

Motion around a central axis such that an object could repeatedly pass the same point in space relative to that axis.

Lever arm

The length of an imaginary line drawn from the axis of rotation to the point at which the force is being applied.

Torque

The tendency of a force to cause rotational acceleration. The magnitude of the torque is equal to the length of the lever arm times the component of the force that is applied perpendicular to it.

Rotational equilibrium

The state in which the sum of the torques acting on an object is zero.

Rule 6.1 (Magnitude of translational acceleration and rotational acceleration)

The magnitude of the forces applied to an object determines the amount of translational acceleration that will occur. The amount of torque applied to an object determines the amount of rotational acceleration that will occur.

When do you ignore an object's weight?

When dealing with rotational equilibrium, always ignore the weight of the object that is rotating.

Rule 6.2 (torques: positive or negative?)

Torques that cause clockwise motion are considered negative torques, while torques that cause counterclockwise motion are considered positive torques.

SI Unit for torque

Newton x meter

Centripetal Force

The force necessary to make an object move in a circle. It is directed towards the centre of the circle.

Centripetal Acceleration

The acceleration caused by centripetal force.

Gravity

The attractive force that exists between all objects which have mass.

Period (T)

The time it takes for an object in uniform circular motion to travel through one complete circle.

Frequency (f)

The number of times per second an object in uniform circular motion travels around the circle.

Rotational Equilibrium

The state in which the sum of the torques acting on an object is zero.

Acceleration of objects in uniform circular motion

Objects in uniform circular motion have a non-zero acceleration, because direction changes, which means that velocity changes, and acceleration is the time rate of change of an object's velocity.

Directions of the velocity and acceleration in uniform circular motion.

When an object is in uniform circular motion, the velocity is always tangent to the circle in which the object is traveling. The acceleration, however, is always directed into the circle, along the radius.

Force and torque in uniform circular motion

In uniform circular motion, there is a force parallel to the lever arm. This means that there is a force directed towards the centre of the circle in which the object moves. Because the force is parallel to the lever arm, there is no net torque, because torque requires a force perpendicular to the lever arm.

Rotational equilibrium in uniform circular motion

Since the sum of the torques in uniform circular motion is zero, the object in motion will be in rotational equilibrium.

Centripetal force in uniform circular motion

The centripetal force is directed toward the centre of the circle in which the object moves, and is necessary for any kind of circular motion.

Centripetal Force

The force that is necessary for any kind of circular motion

Centrifugal force

Isn't a real force at all. Don't confuse it with centripetal force.

Equation 7.4: Relationship of period and frequency.

F=1/T

Hertz (Hz)

1/sec