**Enduring Understanding 3.A π¨βπ»**

All forces share certain common characteristics when considered by observers in inertial reference frames. (A frame of reference in which a body remains at rest or moves with constant linear velocity unless acted upon by forces)

**Essential Knowledge 3.A.1 π**

An observer in a reference frame can describe the motion of an object using such quantities as **position, displacement, distance, velocity, speed, **and **acceleration.**

For rotational motion we define these quantities in terms of **radians** instead of meters.

**The Radian**

Imagine taking the radius of a circle and wrap it around the circumference. It will create an angle whose arc length is equal to the radius. The angle that is created is **1 Radian**.

An angle of π radians would have an arc length of half the circumference and a full circumference would have an angle of 2π radians.

**Basic Rotational Quantities**

**Angular Displacement** - represented by the angle π in radians

**Angular Velocity** - change in angular displacement over time. It can also be calculated from the frequency of the objectβs rotation.

**Angular Acceleration** - change in angular velocity over time.

**All of the linear terms can be related to their rotational term by the following equations (r = radius of the circle). These are NOT on the reference table.**

**Mathematical Representations of Motion π**

In Kinematics there are four major equations you must understand to begin calculations. They relate **acceleration, displacement, initial and final velocity, **and **time **together**.**

**Variable Interpretation:** Ξπ is angular displacement in radians, π is final angular velocity in radians/second, πo is initial angular velocity in radians/second, t is time in seconds, and πΌ is acceleration in rad/s^2.

βΆ In order to solve for a variable without having all four other quantities known, we look at the βVariable Missingβ column to pick the equation that best suits our question.

π₯

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