04Class 11 Physics

Laws of Motion formulas

Newton's laws, friction and circular motion formulas for Laws of Motion. A clean free-body diagram solves most of these problems before any formula does.

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Newton's laws and momentum

Second law: $\displaystyle \vec F = \frac{d\vec p}{dt} = m\vec a$
The form with a holds when mass is constant.
Momentum: $\displaystyle \vec p = m\vec v$
Impulse: $\displaystyle \vec J = \vec F\,\Delta t = \Delta\vec p$
Conservation of momentum: $\displaystyle m_1\vec u_1 + m_2\vec u_2 = m_1\vec v_1 + m_2\vec v_2$
Holds when net external force is zero.

Friction

Limiting static friction: $\displaystyle f_{s,\max} = \mu_s N$
Kinetic friction: $\displaystyle f_k = \mu_k N$
Block on a rough incline: $\displaystyle a = g(\sin\theta - \mu_k\cos\theta)$
Sliding down. It only slides if tan θ exceeds μₛ.

Circular motion

Centripetal force: $\displaystyle F_c = \frac{mv^2}{r}$
Maximum speed on a level road: $\displaystyle v_{\max} = \sqrt{\mu_s r g}$
Ideal speed on a banked road: $\displaystyle v_0 = \sqrt{r g \tan\theta}$
No friction needed at this speed.
Maximum speed on a banked road: $\displaystyle v_{\max} = \sqrt{r g\,\frac{\mu_s + \tan\theta}{1 - \mu_s\tan\theta}}$

Where students slip up

Always writing friction as μN. Static friction only reaches μₛN at the limit, and below that it equals whatever force it balances.
Treating action and reaction as balancing each other. They act on different bodies, so they never cancel on one free-body diagram.
Adding a separate centripetal force to the diagram. It's the name for the net inward force, not an extra one.

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