PHYS CH 8 Rotational Motion Summary

What is circular motion?

Motion in a circular path. Even at a constant speed, motion changes, so acceleration exist

Rotational (angular) speed

Measures how fast something rotates. Same for all points on a rigid object (object that does not flex or change shape).

Rotational (angular) speed units

Rotations/s or radians/s

What letter represents Tangential Speed

v

What letter represents Rotational speed or Angular speed

w (omega)

What is Tangential Speed?

Linear Speed along the circle

What is an example of (tangential) linear speed?

A person running around a circle

Equation for tangential speed ?

v = r x (omega)

What is another name for Rotational speed?

Angular speed

what is another name for tangential speed?

linear speed

Linear-rotational relationship

v = 2π x f which means one full rotation = 2πr distance or circumference x distance

what is the equation to get omega

omega = angle/time

Centripetal force

Force towards the center

Centripetal force equation

F_c = mv²/r

What does centripetal force do?

It keeps objects moving in a circle

What is Centrifugal force?

Apparent outward force in rotating systems, object actually moves tangent if force disappears

Newton’s first law

Without a force, an object is in a straight line, circular motion requires inward force

What is simulated gravity?

Spinning systems create artificial gravity

Simulated gravity equation

a = v²/r ≈ g

What are the four key equations when it comes to circular motion

v = r (omega) - Tangential speed

v = 2πr x f - Linear rotational relationship

F_c = mv²/r - centripetal force

a = v²/ r - simulated gravity

What are the big ideas around rotational motion?

Circular Motion requires constant inward force.

Velocity is tangent, force is inward