Horizontal Circular Motion and Friction
a_r=v^2/r=omega^2 r inward; on a level rough surface mv^2/r <= mu_s mg.
Why this shows up in the exam
Level-road turns · Rotating discs · Circular grooves
Learn the idea
The inward net force is mv squared over r; centripetal force is a role, not a new force. Friction, tension, or a wall normal can supply the required inward acceleration.
🧠 Memory hook: Name the real force pointing inward.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- a_r = v²/r = omega² r — radial acceleration
- F_radial = m v²/r — net inward force
- omega_max = sqrt(mu_s g/r) — horizontal no-slip limit
How to approach it
- 1Choose inward positive
- 2Resolve real forces
- 3Set inward sum to mv²/r
Common slip-ups that cost marks
- •Adding a centripetal force
- •Outward force in inertial frame
- •Using kinetic friction before slip
🌟 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.
Circular motion and centripetal force
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.