PhysicsCircular Motion

Effective Study Strategies

• Understand angular vs linear quantities: θ (angular displacement), ω (angular velocity), α (angular acceleration) are rotational analogs of s, v, a.
• Master the right-hand rule: Curl fingers in direction of rotation, thumb points in direction of angular vector quantities.
• Relate linear and angular motion: v = rω, a_t = rα, a_c = v²/r = rω².
• Practice circular motion equations: Similar to linear motion: ω_f = ω_i + αt, θ = ω_i t + ½αt², ω_f² = ω_i² + 2αθ.
• Differentiate centripetal vs centrifugal: Centripetal force is real (toward center), centrifugal is apparent (away from center in rotating frame).
• Apply conservation of angular momentum: L = Iω = constant if no external torque. I₁ω₁ = I₂ω₂.
• Calculate moment of inertia: I = Σmr². Know values for common shapes: hoop (mr²), disk (½mr²), sphere (⅖mr²).
• Understand satellite dynamics: Orbital velocity v₀ = √(GM/r), critical velocity = 7.9 km/s, geostationary orbit at 36000 km.

Exam Preparation Tips

• Memorize key formulas: Centripetal force F_c = mv²/r = mrω², Angular momentum L = Iω, Rotational KE = ½Iω².
• Practice conversion between units: Radians to degrees (×180/π), revolutions to radians (×2π).
• Solve rolling motion problems: Total KE = ½mv² + ½Iω². For rolling without slipping: v = rω.
• Work with vector cross products: L = r × p, τ = r × F. Direction from right-hand rule.
• Calculate satellite parameters: Orbital period T = 2π√(r³/GM), geostationary T = 24 hours.
• Practice apparent weight problems: In elevators: T = mg ± ma. In satellites: weightless (free fall).

Common Pitfalls to Avoid

• Confusing angular velocity ω (rad/s) with frequency f (Hz) or period T (s)
• Forgetting centripetal force is net force toward center, not an additional force
• Mixing up moment of inertia formulas for different shapes
• Using linear equations when angular equations are needed (or vice versa)
• Confusing geostationary satellites (fixed position) with other satellites
• Forgetting that angular momentum is conserved only if no external torque
• Not using right-hand rule correctly for vector direction
• Confusing real weight (mg) with apparent weight (spring balance reading)