Department

Physics and AstrophysicsCourse Code

PHYA10H3Professor

Brian WilsonStudy Guide

FinalThis

**preview**shows half of the first page. to view the full**1 pages of the document.**How to solve almost any mechanics (not waves) question in PHYA10

Is there a collision? Yes: If only one moving object: use impulse. Δp = Fav Δt and you are done

If more than one moving object: conserve momentum. Δp = 0

Is it elastic? Then conserve energy too. ΔK = 0

Do they stick together? Same final velocities.

Otherwise: tricky... but definitely conserve momentum.

Is there one moving object? Yes: Circular motion? Yes: ar = v2 / R

Uniform circular motion: at = 0

Non-uniform: conserve energy unless it asks about time.

Time? θ(t) = θ0 + ω t + ½ α t2

Parabolic/Projectile motion? Yes: Conserve energy if possible.

Otherwise: x(t) = x0 + v0 t + ½ a t2 (ax = 0 ?)

Oscillation? Yes: ω2 = k/m (assuming mass and spring)

x = xeq + A cos(ω t + φ0)

vx = - A ω sin (ω t + φ0)

Try to use energy conservation.

Vertical springs are tricky: mg = k Δxeq

Linear? Yes: Try to use energy conservation or work

W = ΔE = ΔK + ΔU

Didn't work? v(t) = ∫ a(t) dt and x(t) = ∫ v(t) dt

Constant a? x(t) = x0 + v0 t + ½ a t2

Don't know a? Use Newton's Laws.

Newton's Laws: 1: Always choose a reference frame which is not accelerating.

2: Fnet = ∑ Fi = ma

3: Fa on b = -Fb on a (in other words, every force is an action between two objects)

Might the object rotate? Yes: τnet = ∑ τi = I α

τ = r x F = r F sin θ (use right hand rule for direction of τ)

Equilibrium if the net torque is zero.

Also need to use Newton's Laws.

Kinetic energy might be useful: K = ½ I ω2

Force examples: gravity: mg or GMm/r2

spring: -k Δx

friction: μs N or ≤ μk N

tension or normal: as needed (no equation possible)

Tension has the same magnitude everywhere unless pulley has mass/friction

Energy examples: kinetic: K = ½ m v2 or ½ I ω2

gravity: U = mgy or -GMm/r

spring: U = ½ k (Δx)2

constant force F: W = F ∙ Δd (component of F in the direction of displacement)

###### You're Reading a Preview

Unlock to view full version