6. Chapter Six: Uniform Circular Motion, Newton's Law of Gravitation, and Rotational Motion | AP Physics 1 Review Book

Universal Gravitational Constant

A constant, denoted by the letter "G" in Newton's Law of Gravitation, that is directly related to the force of gravity that is felt between two objects; it is roughly equivalent to 6.67 times 10 to the negative eleventh power Newton-meters.

Fictitious Force

A force that has no physical origin but is merely referenced for hypothetical forces in order to succinctly explain the general patterns of an object's motion.

Torque

A measure of the effectiveness of a force at making an object accelerate rotationally; it is needed to get an object to change its pattern of spin (to either start or stop spinning); it is equivalent to the product of the radius at which the torque is applied, the strength of that force in Newtons, and the sine of the angle at which it is applied; it is represented mathematically as a lowercase tau ("τ") and is measured in Newton-meters, and is thus not (I repeat, not!) categorized as a force.

Banking

A structural design installation in which a curved road or track helps to resist against the extreme centripetal force that an object may feel going around a curve; its ability to resist the centripetal force is dependent upon its angle of incline above the horizontal and its distance from the center of rotation.

Gravitational Force

An attractive force that occurs between any two masses, pulling (always a pulling force!) them together, as a direct resulting of physical law.

Center of Gravity

Another term for the center of mass; this makes sense, as the force of gravity will be concentrated in the location on the object where most of its mass is.

Moment of Inertia

Another term for the rotational inertia of a given object.

Tangential Velocity Vector

Any velocity vector, representing the motion of an object in uniform circular motion, that touches the path of the object, represented as a circle, at only one point; when two of these velocity vectors are added together, with one of the addends being the negative of one of the said velocity vectors, the resultant vector is equivalent to the inwards acceleration resulting from centripetal acceleration.

Tension Force of an Object Causing a Rotation Perpendicular to the Nearest Radius of Said Object

That when a force is exerted to rotate an object that forms a tangent line that is perpendicular to the radius that it intersects, its torque can be found by simply multiplying the radius and the tension force, as the sine of 90° is simply equal to one; all masses dangling from a pulley must follow this rule.

Centripetal Acceleration

The acceleration that occurs in uniform circular motion that changes the direction of the velocity of an object so that it constantly curves inwards; it is often represented as "a[subscript]c" and is set equal to the square of the velocity at which the object moves divided by the radius of its circular path.

Centrifugal Acceleration

The acceleration that occurs in uniform circular motion that changes the direction of the velocity of an object so that it constantly curves outwards.

Action-Reaction Pair of Gravity

The action-reaction pair that results as a direct byproduct of gravitational force in which one object pulls upon another and another pulls upon one; for example, a book resting on a table pulls upon the Earth (very weakly) while the Earth also pulls upon the book (much more strongly).

Acceleration Due to Earth's Gravity

The downwards acceleration that any object at Earth feels at any time as a result of the gravitational pull of the Earth; it is represented mathematically using the lowercase letter "g" and is roughly equivalent to 9.8 meters per second squared.

The "Big Five" Rotational Kinematic Equations

The five primary equations in rotational kinematics that are often used to describe the motion of an object as a direct result of its torque, "τ", moment of inertia, "𝘐", angular acceleration, "α", angular velocity, "ω", and angular displacement, "Δθ"; they can be related directly to the "Big Five" of linear kinematics.

Centrifugal Force

The force that occurs in uniform circular motion that is a result of the centrifugal acceleration, pushing the object outwards away from the center of rotation; by definition, it can never do work, as it always acts perpendicular to the direction of the object's motion; it is a fictitious force, as it is not a real force but is merely the sum of all of the forces acting upon an object that compel it to stay in a circular path.

Centripetal Force

The force that occurs in uniform circular motion that is a result of the centripetal acceleration, pulling the object inwards towards the center of rotation; by definition, it can never do work, as it always acts perpendicular to the direction of the object's motion; it is a fictitious force, as it is not a real force but is merely the sum of all of the forces acting upon an object that compel it to stay in a circular path; it is equivalent to the centripetal acceleration multiplied by the mass of an object (this comes from Newton's Second Law).

The "Right Hand Rule" of Angular Velocity

The general "trick" that is often used in physics in which the direction of angular velocity, either into the page ("⨂") or out of the page ("⊙") can be found by making a cupped "thumbs-up" with one's right hand and orienting it so that the fingers point in the direction of the angular velocity, with the thumb either pointing into our out of the page.

The "Right Hand Rule" of Torque

The general "trick" that is often used in physics in which the direction of torque, either into the page ("⨂") or out of the page ("⊙") can be found by making a cupped "thumbs-up" with one's right hand and orienting it so that the fingers point in the direction of the angular acceleration, with the thumb either pointing into our out of the page.

Equilibrium

The general state at which an object is at both rotational and translational equilibrium; for example, if a stopped or constantly spinning wheel is placed on the ground and left there, it is at equilibrium, as it is not moving left, right, up, down, in, or out and is not slowing down or speeding up.

Static Equilibrium

The general state at which an object is at equilibrium and is, more specifically, not moving at all; it is completely stationary.

Absolute Gravitational Acceleration

The gravitational acceleration that is a result of the gravity of the Earth alone, without the centripetal force of its spinning being taken into account; it is very slightly smaller than the measured gravitational acceleration of "g"; it is often represented as "g[subscript]0".

Measured Gravitational Acceleration

The gravitational acceleration that is the true gravitational acceleration of the Earth (known as absolute gravitational acceleration, or "g[subscript]0") in addition to the minute pulling force of the Earth's centripetal acceleration; it is often very slightly larger than the absolute gravitational acceleration and is represented mathematically as "g".

Newton's Law of Gravitation

The law of gravitation, developed by Sir Isaac Newton, that indicates that the force of gravity that exists between two masses is equivalent to the product of the universal gravitational constant and the two masses divided by the square of the distance between the two masses.

Conservation of Angular Momentum

The law of physics that demonstrates that when no external forces are introduced into a closed system of rotation(s), its angular momentum must be preserved in all circumstances.

Angular Momentum

The momentum of a rotating object that can be set equivalent to the product of the angular momentum and the angular velocity; when divided by the change in time over a given period, the change in it is also equivalent to the torque applied; like linear momentum, it is always conserved in a closed system.

Uniform Circular Motion

The movement of an object, represented as a single particle, around a central point in a perfectly circular path at a constant speed, with acceleration changing its direction only and not its speed.

Geosynchronous Orbit

The orbit in which a satellite's rate of rotation is exactly equivalent to that of the Earth at a given point; as a result of this, it stays in a fixed position above the location of the Earth; all geosynchronous orbiting satellites are approximately 36,000 kilometers above Earth's surface.

Physics of a "Loop-the-Loop"

The physical properties of a looping section of a roller coaster in which a centripetal force is continually felt that is equivalent to the difference of the normal force and the force of gravity.

Center of Mass

The point in an object that moves as if all of the object's mass is concentrated in it and it alone; in homogenous objects, it is simply the geometric center of a three-dimensional shape, while the process of finding it in non-homogeneous shapes is a bit more tricky; it is comparable to the center of gravity (they are roughly the same thing).

Angular Velocity

The rate of change of angular displacement of a rotating body with respect to time; it is set equivalent to the change in the angle (in revolutions) divided by the time passed (in second or minutes) and is often represented mathematically using a lowercase omega, "ω"; it is usually measured in either radians per second or revolutions per minute; note that it is a velocity vector and has both speed and direction!

Angular Acceleration

The rate of change of angular velocity in respect to time; it can be calculated by finding the angular velocity of a given rotating object changes divided by the general elapsed time; it is often represented mathematically using a lowercase alpha ("α"); it is usually measured in radians per seconds squared.

Relationship Between the Torque Applied to an Object and its Rotational Acceleration and Rotational Inertia

The relationship between the torque that is applied to an object and its rotational acceleration and rotational inertia in which a greater rotational inertia, to which a constant torque is applied, will correspond to a lesser rotational acceleration, and vice versa; this is derived from the fundamental mathematical relationship that the torque of a rotating object is equivalent to the product of its rotational inertia and rotational acceleration.

Relationship Between Centripetal Radius and Centripetal Force

The relationship by which a decrease in radius increased the centripetal force that an object feels, and vice versa; as the circular path of an object continually draws smaller and smaller, eventually, there will come a point at which it is too great to be resisted by friction, and the object will slip.

Relationship Between Angular Position and Arc Length

The relationship by which the distance travelled around the circle (the displacement) is equivalent to the angle, in radians, of which the arc is created multiplied by the radius of the circle.

Relationship Between the Distribution of Mass in an Object and its Rotational Inertia

The relationship existing between the distribution of mass in an object and its rotational inertia in which an object with the majority of its mass being "spread out" further from its axis of rotation will generally have a greater rotational inertia that an object with the majority of its mass being "condensed in" towards its axis of rotation; this is why figure skaters pull their arms in when they spin, as concentrating their mass closer to their axis of rotation means a lesser rotational inertia, allowing them to spin more quickly (angular acceleration) with the same amount of torque.

Relationship Between Positioning of a Mass and its Angular Momentum

The relationship in physics by which a greater rotational velocity can be achieved with a mass closed to the axis of rotation to an object; and vice versa, this plays into angular momentum and the natural law dictating its conservation.

Rotational Equilibrium

The state in which all of the rotational forces acting upon an object are equivalent to zero; when in this state, while not necessarily not spinning, an object is not speeding up or slowing down rotationally, as all of its forces cancel each other out.

Translational Equilibrium

The state in which the sum of all of the forces acting upon an object is equivalent to zero; when in this state, an object is not increasing or decreasing in height or distance in both the x- and y-coordinate directions.

Rotational Kinematics

The study of the movement of objects in a rotational fashion that acts one dimensional in the sense that the only dimension along which motion can occur is along that of a circle.

Net Torque

The sum of all of the torques acting upon an object; please be careful and note that torques acting in opposite directions must have a situation in which at least one of them is negative (there will be a difference).

Rotational Inertia

The tendency of a rotating object to remain rotating at its current speed unless any kind of acceleration or decelerating force is applied to it.