03Class 11 Physics

Motion in a Plane formulas

Vectors, projectile motion and circular motion formulas for Motion in a Plane. Split every 2D problem into x and y parts.

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All Physics formulas

Vectors

Resultant of two vectors: $\displaystyle R = \sqrt{A^2 + B^2 + 2AB\cos\theta}$
Direction of the resultant: $\displaystyle \tan\alpha = \frac{B\sin\theta}{A + B\cos\theta}$
α is the angle from A.
Components: $\displaystyle A_x = A\cos\theta, \quad A_y = A\sin\theta$

Projectile motion

Time of flight: $\displaystyle T = \frac{2u\sin\theta}{g}$
Maximum height: $\displaystyle H = \frac{u^2\sin^2\theta}{2g}$
Horizontal range: $\displaystyle R = \frac{u^2\sin 2\theta}{g}$
Largest at θ = 45°. Angles θ and 90° − θ give the same range.
Path equation: $\displaystyle y = x\tan\theta - \frac{g x^2}{2u^2\cos^2\theta}$

Circular motion

Angular speed: $\displaystyle \omega = \frac{\Delta\theta}{\Delta t} = \frac{2\pi}{T} = 2\pi\nu$
Linear and angular speed: $\displaystyle v = r\omega$
Centripetal acceleration: $\displaystyle a_c = \frac{v^2}{r} = r\omega^2$

Where students slip up

Using the range and height formulas when launch and landing heights differ. They only hold when both are at the same level.
Measuring θ from the vertical. The formulas here use the angle from the horizontal.
Forgetting that the vertical velocity is zero at the top, while the horizontal velocity stays the same throughout.

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