Vertical Circles and Contact Loss
At every point sum F_inward=mv^2/r; for a smooth fixed track mechanical energy is conserved.
Why this shows up in the exam
Vertical circles · Curved tracks · Pendulum tension
Learn the idea
Use energy for speed and radial force balance for tension or normal reaction. Gravity’s radial component changes around a vertical path; contact ends when N or T would become negative.
🧠 Memory hook: Energy gives speed; radial balance gives contact.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- sum F_inward = m v²/r — radial equation
- v²=u²+2g(h_i-h) — smooth-track energy
- N=0 or T=0 — limiting contact
How to approach it
- 1Find speed
- 2Draw inward components
- 3Apply radial balance and test contact
Common slip-ups that cost marks
- •Centripetal as extra force
- •Assuming constant speed
- •Accepting negative contact force
🌟 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?
More from Laws of Motion
Newton's laws of motion
Understand and apply Newton's first, second, and third laws to analyze forces, motion, and interactions in various physical situations.
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Analyze the forces involved in uniform and non-uniform circular motion, including centripetal force, tension, and friction.
Friction and its applications
Study the types of friction (static and kinetic), their effects on motion, and how friction interacts with other forces in different scenarios.
Impulse, momentum, and conservation laws
Explore the principles of linear momentum, impulse, and their conservation in collisions and explosions.
Inertia and Inertial Frames
In an inertial frame, sum F_ext = 0 implies a = 0. Earth-fixed frames are approximate when rotational effects are negligible.
Newton’s Second Law in Vector Form
In an inertial frame sum F_ext = dp/dt; for constant mass this becomes m dv/dt = ma.