Flash Cards

In this article, we have attempted to teach you the formulas for projectile motion by presenting some solved examples. Through this method, you will gain a better understanding of the equations for projectiles. Definition of projectile motion: Projectile motion refers to the motion of any object that is thrown into the air at an angle $\theta$. It is characterized by motion in two dimensions and is solely influenced by gravitational force.  Projectile Motion Formulas: The following equations represent projectile motion in the vertical and horizontal directions. In the horizontal direction: \begin{align*} \text{Displacement}&:\,\Delta x=\underbrace{\left(v_0 \c

How to find acceleration from a position vs. time graph?  Answer: in one word, the shape of the graph shows the acceleration. A straight line means zero acceleration. A curved line means non-zero acceleration. The steeper the curve, the bigger the acceleration. A bowl shape means positive acceleration (speeding up). An upside-down bowl means negative acceleration (slowing down).  In this article, you will learn how to find the acceleration from the position-time graph, both graphically and numerically, with some solved problems for grade 12 or college level.  You can skip this introduction and refer to the worked examples.    Types of Motion: An o

The helical path is the path of the motion of a charged particle when enters at an angle of $\theta$ in a uniform magnetic field $B$. In this short tutorial, we explain the factors that cause this type of motion. On a moving charged particle in a uniform magnetic field, a magnetic force of magnitude $F_B=qvB\,\sin \theta$ is acted where $\theta$ is the angle of velocity vector $v$ with the magnetic field vector $B$. This is the main factor that creates a spiral or helical path.  A charged particle (say, electron) can enter a region filled with uniform $B$ either with right angle $\theta=90^\circ$ or at angle $\theta$. In the former case, its path results in a ci

Problems and Solutions about displacement and distance are presented which is helpful for high school and college students. In the following, displacement is computed for simple cases.   Displacement Problems: Problem (1): An object moves from point A to B, C, and D finally, along a rectangle.  (a) Find the magnitude and direction of the displacement vector of the object? (b) Find the distance traveled by that object? (c) Suppose the object returns to point A, its initial position. Now, Find the displacement and distance. Solution: (a) By definition of displacement, connect the initial (A) and final (D) points together. As shown, displace

The direction of the magnetic force on a moving positively charged particle or a wire carrying current $i$ in a uniform magnetic field is determined by the right-hand rules with different versions stated below.  Version 1 (right-hand rule): point the fingers of your right hand in the direction of $\vec v$ and curl them (through the smaller angle) toward $\vec B$. Your upright thumb shows the cross product $\vec v \times \vec B$ or the magnetic force $\vec F_B$. This force is perpendicular to the plane of $\vec v-\vec B$ Version 2 (right-hand rule): point your fingers in the direction of $\vec B$ so that the thumb points toward the velocity $\vec v$, your palm shows the direct

The comparison between electric and magnetic forces in physics for high school students is presented briefly.  Definition and formulas: Electric force is repulsion or attraction between two charged objects or particles, moving or at rest, and is calculated by Coulomb’s law with the following formula  \[\vec{F}_E =k\,\frac{|q|\,|q^{'}|}{r^{2}}\,\hat{r}\] where $\hat{r}$ is the unit vector that indicates the direction of the electric force and $r$ is the distance between the two charges. According to Coulomb's law, this force is proportional to the product of the magnitudes of the charges that are $|q|$ and $|q'|$. But magnetic force is a repulsion