Laws of Motion — MHT-CET Physics

Formulas (3)

• Lifts, Blocks in Contact and Pulleys · Second law
  $$\sum \vec{F} = m\vec{a}, \qquad N_{\text{lift}} = m(g \pm a)$$
• Force, Work, Power and Circular Dynamics · Work and power
  $$W = \vec{F}\cdot\vec{r}, \qquad P = \vec{F}\cdot\vec{v}, \qquad F_c = \frac{mv^2}{r}$$
• Braking, Penetration and Avoiding Collision · Uniform retardation
  $$v^2 = u^2 - 2as, \qquad s_{\text{safe}} = \frac{(v_A - v_B)^2}{2a}$$

Watch out for (6)

• Subtracting a for a lift accelerating up
  → Lifts, Blocks in Contact and Pulleys
• Using the applied force for the far block
  → Lifts, Blocks in Contact and Pulleys
• Taking tension at the bottom as mg
  → Force, Work, Power and Circular Dynamics
• Using average power for power at an instant
  → Force, Work, Power and Circular Dynamics
• Assuming speed falls linearly with distance
  → Braking, Penetration and Avoiding Collision
• Using each car's own stopping distance
  → Braking, Penetration and Avoiding Collision

Formulas (2)

• Impulse and Rates of Momentum · Impulse
  $$\vec{J} = \int \vec{F}\,dt = \Delta\vec{p}, \qquad F = \frac{dp}{dt}$$
• Collisions and the Coefficient of Restitution · Restitution
  $$e = \frac{v_2 - v_1}{u_1 - u_2}$$

Watch out for (4)

• Forgetting the rebound doubles the change
  → Impulse and Rates of Momentum
• Adding the areas of a force graph without their signs
  → Impulse and Rates of Momentum
• Rebound height e·h
  → Collisions and the Coefficient of Restitution
• Conserving kinetic energy in every collision
  → Collisions and the Coefficient of Restitution

Formulas (1)

• Moments, Reactions and the Centre of Mass · Equilibrium and CM
  $$\sum\vec{F} = 0, \quad \sum\tau = 0, \qquad x_{cm} = \frac{m_1x_1 + m_2x_2}{m_1 + m_2}$$

Watch out for (2)

• Taking moments about the wrong point
  → Moments, Reactions and the Centre of Mass
• Placing the centre of mass at the midpoint
  → Moments, Reactions and the Centre of Mass