Understanding Rotational Motion and Forces

axis

An axis is an imaginary line around which an object rotates.

rotation

Rotation is the spinning of an object around its own axis.

revolution

Revolution is the movement of an object around another object.

rotational speed symbol

ω (omega)

rotational speed unit

Radians per second (rad/s) or revolutions per minute (RPM)

rotational speed and radius

It stays the same for all points on a rotating object.

tangential/linear speed symbol

v

tangential/linear speed unit

Meters per second (m/s)

tangential speed and radius

It increases with a larger radius (v = ωr).

tangential speed and rotational speed relationship

Tangential speed = rotational speed × radius (v = ωr).

tangential speed and rotational speed

They are directly proportional.

RPM

Revolutions per minute

RPM usage

RPM is used for rotational speed.

RPM conversion

Radians per second (rad/s)

rotational inertia effect

Larger rotational inertia makes it harder to start or stop rotation.

rotational inertia dependence

Mass and the distribution of mass from the axis.

torque cause

Rotation

torque dependence

Force and lever arm length

increase torque

Apply more force; increase the lever arm length.

torque unit

Newton-meters (N·m)

torque directions

Clockwise or counterclockwise

balanced torque condition

If clockwise torque = counterclockwise torque, the object is balanced.

lever arm measurement

From the axis of rotation to the point where the force is applied.

lever arm effect

Easier

force direction for torque

Perpendicular

center of mass/gravity

The point where all the mass or weight of an object is concentrated.

center of gravity dependency

It depends on the shape and mass distribution of the object.

center of gravity explanations

Stability of objects; balance and toppling behavior

CG mass existence

No

Toppling Rule

An object will topple if its center of gravity falls outside its base of support.

centripetal force reality

Real

centripetal force direction

Toward the center of the circular path

centrifugal force reality

Fake (it's a fictitious force from the perspective of the rotating frame)

centrifugal force direction

Outward from the center (from the rotating object's perspective)

centrifugal force cause

It's a perceived effect caused by inertia in a rotating frame.

outward force sensation

Your body resists the inward acceleration due to inertia, creating the sensation of an outward force.

centripetal force examples

Gravity keeping planets in orbit; tension in a spinning ball on a string

centrifugal force examples

Feeling pushed outward in a car turning sharply; clothes pressing outward in a spin dryer

simulated gravity creation

By spinning a space station to create centripetal force that mimics gravity.

simulated gravity necessity

To prevent muscle and bone loss and help with orientation and health.