Types of Motion: Translational and Rotational

Practice flashcards covering the definitions, formulas, and relationships of translational and rotational motion as discussed in the lecture notes.

Motion

Movement of a body either rectilinear or curvilinear.

Translational Motion

Motion of a body moving along the same direction, distance, and time.

Rotational Motion

Movement of an object around a central point, spinning on its either moving or fixed axis.

Displacement

A vector quantity of the change in position of the object, measured with the unit $m$.

Angular Displacement

The angle through which an object or point rotates about an axis, measured with the unit $rad$.

Linear Velocity ($V$)

The rate of the change in displacement over time on a straight path, measured with the unit $m/s$.

Angular Velocity ($W$)

The rate of the change in angular position of a rotating body, measured with the unit $rad/s$.

Angular Velocity Formulas

Calculated as 1.) $w = \frac{\theta}{t}$, 2.) $w = \pi t$, and 3.) $w = \frac{v}{r}$, where $\theta$ is position angle, $t$ is time, and $v$ is linear velocity.

Relationship of Linear and Rotational Velocity

Defined by the equation $V_t = r \times w$, where bigger rotating objects will result in higher linear velocity.

Acceleration

The rate at which an object changes its velocity, measured with the unit $m/s^2$.

Angular Acceleration

The rate at which angular velocity changes over time, measured with the unit $rad/s^2$.

Linear and Rotational Kinematics Equations

The set of formulas including $V_f = v_i + at$ and $\Delta x = v_i t + \frac{1}{2} at^2$ for linear motion, and $w_f = w_i + \alpha t$ and $\Delta \theta = w_i t + \frac{1}{2} \alpha t^2$ for rotational motion.

Size and Spin Relationship

Bigger rotating objects are slower to spin and vice versa.