Catapult Physics: Forces, Motion, and Energy

A set of vocabulary flashcards covering the forces, kinematics, rotational dynamics, and energy principles involved in a catapult mechanism based on the lecture notes.

Normal Force

A support force that one surface exerts on another surface in contact with it, acting perpendicular to the contact surface. It is a vector measured in Newtons ($\text{N}$), represented by the formula $F_N = mg$ for a simple object resting on a horizontal surface with no other vertical forces.

Friction

A force that opposes intended motion between two touching surfaces, caused by the molecular roughness of the surfaces.

Static Friction

The force that prevents two touching surfaces from beginning to slide against each other when they are not moving relative to each other. It is a vector measured in Newtons ($\text{N}$) given by the formula $f_s \le \mu_s F_N$.

Kinetic Friction

The force that opposes motion when two touching surfaces are sliding against each other. It is a vector measured in Newtons ($\text{N}$) given by the formula $f_k = \mu_k F_N$.

Tension

A pulling force transmitted through a rope, cord, cable, or elastic band trying to go back to its original shape. It is a vector measured in Newtons ($\text{N}$) that can pull but cannot push because flexible materials go slack when pushed, contributing to net force via $\sum F = ma$.

Spring Force

A force exerted by a stretched or compressed material that tends to return to its original shape. It is a vector measured in Newtons ($\text{N}$) modeled by Hooke's Law as $F_s = -kx$.

Torque

A twisting effect caused by a force that causes angular acceleration around an axis or a pivot point. It is a vector represented by the Greek letter tau ($\tau$) with units of Newton-meter ($\text{N}\cdot\text{m}$), given by $\tau = rF\sin(\theta)$ and $\sum \tau = I\alpha$.

Rotational Inertia ($I$)

A measure of how difficult it is to change an object's rotation, appearing in the rotational dynamics equation $\sum \tau = I\alpha$.

Air Resistance

A type of fluid friction that opposes an object’s motion through air. It is a vector measured in Newtons ($\text{N}$) defined by the formula $F_{air} = -bv$, where $b$ is a constant describing the effect of air resistance and $v$ is velocity.

Linear Acceleration

The rate at which an object’s velocity changes, describing how quickly it speeds up, slows down, or changes direction in a straight line. It is a vector represented by $a$ with units of $m/s^2$, calculated as $a = \frac{\Delta v}{\Delta t} = \frac{v_f - v_i}{\Delta t}$ and $a = \frac{F_{net}}{m}$.

Angular Acceleration

The rate at which angular velocity changes, describing how quickly an object's rotation speeds up, slows down, or changes direction. It is a vector represented by the Greek letter alpha ($\alpha$) with units of radians per second squared ($rad/s^2$), calculated as $\alpha = \frac{\Delta \omega}{\Delta t} = \frac{\omega_f - \omega_i}{\Delta t}$.

Potential Energy

The stored ability to do work based on mass and height. It is a scalar quantity measured in Joules ($\text{J}$).

Gravitational Potential Energy

The energy stored by an object based on its position in a gravitational field, calculated with the formula $U_g = mgh$, where $m$ is mass in kilograms, $g$ is gravitational acceleration ($9.8\,m/s^2$), and $h$ is height above a chosen reference level.

Spring Potential Energy

The energy stored in an elastic material when stretched or compressed, calculated with the formula $U_s = \frac{1}{2}kx^2$, where $k$ is the spring constant describing stiffness and $x$ is the distance stretched or compressed from relaxed length.

Kinetic Energy

The energy an object has because it is moving. It is a scalar quantity measured in Joules ($\text{J}$).

Translational Kinetic Energy

The energy of an object associated with linear motion, given by the formula $K_{trans} = \frac{1}{2}mv^2$, where $m$ is mass in kilograms and $v$ is linear speed in meters per second.

Rotational Kinetic Energy

The energy of an object associated with spinning or rotating motion, given by the formula $K_{rot} = \frac{1}{2}I\omega^2$, where $I$ is the moment of inertia and $\omega$ is angular velocity in radians per second.