Physics_2_Kinematics_and_EnergyPhysics_2_Kinematics_and_EnePhysics_2_Kinematics_and_Energy.pptxrgy.pptx.pptx

Physics_2_Kinematics_and_Energy.pptx

1. Kinematics & Energy Motion in 1D/2D, circular motion, and work–energy methods

2. Kinematics — Core Ideas Position x(t), velocity v(t)=dx/dt, acceleration a(t)=dv/dt. Constant‑a formulas (1D): v = v₀ + at; x = x₀ + v₀t + ½at²; v² = v₀² + 2aΔx. Graph view: slope of x(t) is v; slope of v(t) is a; area under a(t) is Δv.

3. Projectile Motion (2D) Independence: horizontal (ax=0) vs vertical (ay=−g). vx(t)=v₀cosθ (constant), vy(t)=v₀sinθ − gt. y(t)=y₀ + v₀sinθ·t − ½gt²; x(t)=x₀ + v₀cosθ·t. range height Peak: vy=0 ⇒ t_peak = v₀sinθ / g

4. Range & Height (Level Ground) Time of flight: T = 2 v₀ sinθ / g Max height: H = (v₀² sin²θ) / (2g) Range: R = (v₀² sin2θ)/g (no air, same heights)

5. Uniform Circular Motion Speed constant, direction changing ⇒ a points to center. Centripetal acceleration: a_c = v²/r = ω²r Centripetal force: F_c = m v² / r (a requirement, not a new force)

6. Work–Energy Theorem Net work = ΔK = ½ m v² − ½ m v₀² Conservative forces store potential energy U; non‑conservative (friction) dissipate. Energy method often bypasses time to solve speeds and heights.

7. Potential Energy Gravity (near Earth): U_g = m g h Spring: U_s = ½ k x² (measured from natural length) Conservation: K₁ + U₁ + W_nc = K₂ + U₂

8. Power & Efficiency Power: P = dW/dt = F·v (for constant F and v colinear) Average power over interval: W/Δt Efficiency = useful output power / input power

9. Momentum vs Energy — Which Tool? Use momentum (and impulse) for collisions and short forces. Use energy for speed/height problems where forces are conservative. Sometimes both are handy (e.g., inelastic collision + height).

10. Example: Elevated Projectile A ball is thrown at speed v₀ and angle θ from y₀ to a wall at distance L and height H. Solve t from x(t)=L, then plug into y(t) to check if y(L)=H. If you want speed at the wall: v = √(vx² + vy²) with vy = v₀sinθ − g t. L H Tip: keep x and y separate; link with time.

11. Example: Ramp Energy A block slides from height h on a frictionless track ⇒ v_bottom = √(2gh). If friction μ_k acts over distance d: mgh − μ_k m g d = ½ m v². Solve for v or μ_k as needed. Energy avoids solving for time.

12. Common Pitfalls & Tips Track signs for ay (take upward positive unless stated). Angles: confirm whether θ is from the horizontal or another reference. Draw a quick diagram before writing equations. Always sanity‑check units and limiting cases.