Summary - Neet Motion In A Plane

MOTION IN A PLANE
High-Yield Revision Notes & Formula Sheet



1. SCALARS & VECTORS


Dot Product (Scalar Product) Resultant & Direction

$\vec{A} \cdot \vec{B} = AB \cos\theta$
$R = \sqrt{A^2 + B^2 +
Work Done: $W = \vec{F} \cdot \vec{S}$ Magnitude:
2AB\cos\theta}$
Perpendicular Condition: If $\theta = 90^\circ$, then
$\vec{A} \cdot \vec{B} = 0$. $\tan\alpha =
Direction:\frac{B\sin\theta}{A +
Cross Product (Vector Product)
B\cos\theta}$
$\vec{A} \times \vec{B} = (AB \sin\theta) \hat{n}$

Torque: $\vec{\tau} = \vec{r} \times \vec{F}$

Parallel Condition: If $\theta = 0^\circ \text{ or }
Resultant R
180^\circ$, then $\vec{A} \times \vec{B} = 0$. Vector B


Vector A




2. PROJECTILE MOTION (GROUND-TO-GROUND)

Two-dimensional motion under constant vertical acceleration due to gravity ($g$).

Horizontal Component: $u_x = u \cos\theta$
(Constant, $a_x = 0$)

Vertical Component: $u_y = u \sin\theta$ (Variable, u

$a_y = -g$)
H



Time of Flight $T = Range (R)


($T$): \frac{2u\sin\theta}{g}$
Key Points: $R_{\text{max}}$ occurs at $\theta = 45^\circ$.
$H = Complementary angles ($\theta$ and $90^\circ - \theta$)
Max Height
\frac{u^2\sin^2\theta} yield equal range.
($H$):
{2g}$
Horizontal Range $R = \frac{u^2\sin
($R$): 2\theta}{g}$



Equation of Trajectory: $$y = x\tan\theta - \frac{gx^2}{2u^2\cos^2\theta} = x\tan\theta
\left(1 - \frac{x}{R}\right)$$


3. UNIFORM CIRCULAR MOTION (UCM)

REVISION NOTES MOTION IN A PLANE PAGE 1 OF 2