1.
*revolution*: Motion of an object turning around an axis that lies outside the object.
2.
*rotational*: Spinning motion that occurs when an object rotates about an axis located within the object (usually an axis through its center of mass).
3.
*RPM*¹: ¹Physics types usually describe rotational speed, ω, in terms of the number of "radians" turned in a unit of time. There are a little more than 6 radians in a full rotation (2π radians, to be exact). When a direction is assigned to rotational speed, we call it rotational velocity). Rotational velocity is a vector whose magnitude is the rotational speed. By convention, the rotational velocity vector lies along the axis of rotation.
4.
Angular momentum: The product of a body's rotational inertia and rotational velocity about a particular axis. For an object that is small compared with the radial distance, it can be expressed as the product of mass, speed, and the radial distance of rotation.
5.
Angular momentum is defined as the product of rotational inertia and rotational velocity. Like linear momentum, angular momentum is a vector quantity and has direction as well as magnitude.
Angular momentum =: = rotational inertia × rotational velocity
6.
axis (pl. axes): (a) Straight line about which rotation takes place.
(b) Straight lines for reference in a graph, usually the x-axis for measuring horizontal displacement and the y-axis for measuring vertical displacement.
7.
Center of gravity (CG): The average position of weight or the single point associated with an object where the force of gravity can be considered to act.
8.
Center of mass (CM): The average position of the mass of an object. The CM moves as if all the external forces acted at this point.
9.
Centrifugal force: An outward force apparent in a rotating frame of reference. It is apparent (fictitious) in the sense that it is not part of an interaction but is a result of rotation--with no reaction-force counterpart.
10.
Centripetal force: A force directed toward a fixed point, usually the cause of circular motion : F = mv²/r.
11.
Conservation of angular momentum: When no external torque acts on an object or a system of objects, no change of angular momentum can occur. Hence, the angular momentum before an event involving only internal torques or no torques is equal to the angular momentum after the event.
12.
Equilibrium: The state of an object in which it is not acted upon by a net force or a net torque.
13.
For the case of an object that is small compared with the radial distance to its axis of rotation, such as a tin can swinging from a long string or a planet orbiting in a circle around the Sun, the angular momentum can be expressed as the magnitude of its linear momentum, *mv*, multiplied by the radial distance, *r*. In shorthand notation:: Angular momentum = mvr
(also = Iω)
14.
Hoop about diameter:: I = ½ mr²
15.
Hoop about normal axis:: I = mr²
16.
Just as an external net force is required to change the linear momentum of an object, an external net torque is required to change the angular momentum of an object. We can state a rotational version of Newton's first law (the law of inertia):: An object or system of objects will maintain its angular momentum unless acted upon by an external net torque.
17.
Linear momentum = mass × velocity: Angular momentum's counterpart is:
18.
number of rotations or revolutions per unit of time: It is common to express totational rates in revolutions per minute (RPM).
19.
Re call the equilibrium rule in Chapter 2--that the sum of the forces acting on a body or any system must equal zero for mechanical equilibrium. That is, ∑F = 0. We now see an additional condition. The *net torque* on a body or on a system must also be zero for mechanical equilibrium...: ...(∑T = 0, where T stands for torque). Anything in mechanical equilibrium doesn't accelerate--neither linearly nor rotationally.
20.
Rotational inertia (often called moment of inertia): The property of an object that measures its resistance to any change in its state of rotation: if at rest, the body tends to remain at rest; if rotating, it tends to remain rotating and will continue to do so unless acted upon by a external net torque.
21.
Rotational speed (sometimes called angular speed): The number of rotations or revolutions per unit of time; often measured in rotations or revolutions per second or per minute. (Scientists usually measure it in radians per second.)
22.
Simple pendulum:: I = mr²
23.
Solid cylinder:: I = ½ mr²
24.
Solid sphere about CG:: I = 2/5 mr²
25.
Stick about CG:: I = 1/12 mL²
26.
Stick about end:: I = 1/3 mL²
27.
Tangential speed: The linear speed tangent to a curved path, such as in circular motion.
28.
Tangential speed~: ~radial distance × rotational speed.
In symbol form, v ~ rω
29.
The rotational inertia of a pole, or of any object, depends on the axis about which it rotates.⁴: ⁴When the mass of an object is concentrated at the radius r from the axis of rotation (as for a simple pendulum bob or a thing ring), rotational inertia I is equal to the mass m multiplied by the square of the radial distance. For this special case, I = mr².
30.
Torque: The product of force and lever-arm distance, which tends to produce rotation.
Torque = lever arm × force
