Conical Pendulum and Turning Deflection
For steady height, T cos theta=mg and T sin theta=ma_h, so tan theta=a_h/g.
Why this shows up in the exam
Conical pendulums · Turning cars · String accelerometers
Learn the idea
A hanging string tilts so tension supports weight and supplies horizontal acceleration. A turning-car bob and a conical pendulum align with the resultant effective gravity.
🧠 Memory hook: Vertical supports; horizontal turns.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- T cos(theta)=m g — vertical balance
- T sin(theta)=m v²/r — radial balance
- tan(theta)=v²/(r g) — tilt relation
How to approach it
- 1Resolve tension
- 2Write vertical and radial equations
- 3Divide to eliminate T
Common slip-ups that cost marks
- •Angle from wrong axis
- •Setting T=mg
- •Forgetting v squared over r
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A 2 kg block moves on a horizontal rough surface with coefficient of kinetic friction 0.2. A horizontal force of 10 N acts on it. Take g = 10 m/s^2. What is its acceleration?
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