Translational and Rotational Motion

Key vocabulary terms and definitions covering translational motion, rotational motion, and linear and angular dynamics based on the lecture notes.

Translational motion

A type of motion that occurs when an object moves along a path in any of the three dimensions in a straight line, where all parts of the object move the same distance, in the same direction, and at the same time.

Displacement

An object's net change in position, defined as the shortest straight-line distance from its starting point to its final point, along with the direction of that movement.

Average velocity

The overall displacement of an object divided by the total time it took to cover that displacement, calculated as $v_{avg} = \frac{x_f - x_i}{t_f - t_i}$, and measured in $m/s$.

Speed

A scalar quantity describing how fast an object is travelling.

Velocity

A vector quantity describing the speed of an object in a given direction.

Acceleration

The rate at which an object changes its velocity, occurring when an object speeds up, slows down, or changes direction, measured in $m/s^2$.

Uniformly accelerated Motion

A condition where an object's acceleration is constant, allowing for kinematic quantities to be calculated using specific motion equations.

Rotational motion

The circular movement of a rigid object around a fixed central line known as the axis of rotation, where every point moves in a circular path at a constant distance from the axis.

Axis of rotation

The fixed central line around which a rigid object rotates.

Angle of Rotation ($\theta$)

The angular equivalent of distance, measured in radians.

Angular Velocity ($\omega$)

The rate at which an object rotates, typically measured in radians per second ($rad/s$).

Angular Acceleration ($\alpha$)

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

Torque ($\tau$)

The rotational equivalent of force that measures the effectiveness of a force in causing an object to rotate, defined as $\tau = rF\times \text{sin}(\theta)$, where $r$ is the lever arm.

Moment of Inertia ($I$)

The rotational equivalent of mass that depends on an object's mass and how that mass is distributed relative to the axis, calculated as the sum of $mr^2$.

Lever arm ($r$)

The perpendicular distance from the axis of rotation to the point where force is applied, which directly affects the amount of torque produced.