PHYA10H3 Study Guide - Final Guide: Kinetic Energy, Circular Motion
DepartmentPhysics and Astrophysics
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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)
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