Sticking of Person With Wall of Rotor – Complete Notes, Revision, Important Questions & Downloads
Sticking of Person With Wall of Rotor covers the TOC subtopic Minimum Angular Velocity. A person of mass m stands in contact with the inner wall of a cylindrical drum (radius r) that rotates about its vertical axis. When the floor is removed, the person is held against the wall by friction. The centripetal (centrifugal in non-inertial frame) force provides the normal reaction N = mω²r. Friction = μN = μmω²r must support weight mg. Minimum angular velocity: ω_min = √(g/μr). NEET tests this as a direct formula numerical or conceptual question on rotor rides.
NEET Weightage — Sticking of Person With Wall of Rotor
Friction (Chapter 5)| NEET Year | Questions from this Topic | Bar | Marks |
|---|---|---|---|
| 2024 | 1 | 4 | |
| 2023 | 0 | 0 | |
| 2022 | 1 | 4 | |
| 2021 | 0 | 0 | |
| 2020 | 1 | 4 | |
| 2019 | 0 | 0 | |
| 6-Year Total (2019–2024) | 0–2 | 0–8 |
CONDITION: For person to remain on the wall without sliding down: f ≥ mg → μmω²r ≥ mg → μω²r ≥ g → ω² ≥ g/(μr) → ω ≥ √(g/μr). MINIMUM: ω_min = √(g/μr). Mass m cancels — ω_min is mass-independent. Minimum frequency: n_min = ω_min/(2π) = (1/2π)√(g/μr). Minimum time period: T_max = 2π/ω_min = 2π√(μr/g) [the maximum period for which person doesn't slide].
DEPENDENCE: ω_min increases as μ decreases (less friction → need more centrifugal compression). ω_min decreases as r increases (larger drum → need less ω for same centripetal force). ω_min ∝ 1/√(μr). A heavier person and a lighter person need the same ω_min (mass cancels) — consistent with the analogous result in the block-on-cart problem.
How to Solve the Rotor Ride Problem
Step 1 — Write the centripetal force equation The drum wall pushes the person inward to keep them in circular motion: N = mω²r. This is the normal force from the wall on the person.
Step 2 — Write the friction condition Friction (upward) ≥ weight (downward): μN ≥ mg → μmω²r ≥ mg. Cancel m: μω²r ≥ g.
Step 3 — Solve for ω_min ω_min = √(g/μr). Convert to frequency: n_min = ω_min/(2π). Convert to velocity: v_min = ω_min × r = r√(g/μr) = √(gr/μ).
Study Materials — Sticking of Person With Wall of Rotor
PDF · Cheat Sheet · MCQ Set · PYQSubtopics — Sticking of Person With Wall of Rotor
2-Column Table| Column A | Column B |
|---|---|
Rapid Revision — Sticking of Person With Wall of Rotor
Concept → Trap → Example1) Minimum Angular Velocity — Rotor/Drum Problem
Minimum Angular VelocityPROBLEM: A person (mass m) in a cylindrical rotor (inner radius r). The rotor spins vertically about its central axis with angular velocity ω. The floor is removed. Person presses against the wall and is supported by friction. Find the minimum ω for the person not to slide down. INERTIAL (GROUND) FRAME: Person moves in a horizontal circle of radius r with angular velocity ω. Net horizontal centripetal force (inward) = mω²r. Only horizontal force on person = Normal force N from the drum wall. Therefore N = mω²r (directed toward the axis, centripetal). Vertical forces: friction f (upward, from wall) and weight mg (downward). For person to not slide: f ≥ mg. At limiting (minimum) condition: f = μN. So μN ≥ mg → μmω²r ≥ mg. Cancel m: μω²r ≥ g → ω² ≥ g/(μr) → ω ≥ √(g/μr). RESULT: ω_min = √(g/μr). KEY CONVERSIONS: Minimum frequency (revolutions per second): n_min = ω_min/(2π) = [1/(2π)]√(g/μr). Maximum safe period T (above which person slides): T_max = 1/n_min = 2π/ω_min = 2π√(μr/g). Minimum linear speed (tangential): v_min = ω_min × r = r√(g/μr) = √(gr/μ).
- MASS INDEPENDENCE: ω_min = √(g/μr) contains no mass term. Both a 50 kg person and a 100 kg person in the same rotor need the same ω_min. This is because raising mass m increases both the required friction needed (mg) and the available friction (μmω²r) proportionally — the m cancels in the condition μmω²r ≥ mg. In amusement park rotor rides, all passengers (regardless of weight) are safe at the same speed.
- NON-INERTIAL (ROTATING) FRAME: In the frame of the rotor, the person is stationary. Centrifugal force (pseudo-force) = mω²r directed radially outward (away from axis). This presses the person against the wall. Normal force N = mω²r (wall on person, inward) balances the centrifugal force. Friction = μN = μmω²r (upward). Weight = mg (down). Equilibrium: μmω²r = mg → ω = √(g/μr). Both frames give the same ω_min.
- SPEED FORM: v_min = √(gr/μ). This is the minimum tangential speed of the person for sticking. Note: v = ωr, so ω_min = v_min/r = √(gr/μ)/r = √(g/μr) ✓. Larger radius r: v_min increases (more speed needed for larger drum) but ω_min = v/r actually decreases (less angular velocity). NEET sometimes asks for v_min instead of ω_min — use v_min = √(gr/μ) or equivalently v_min = ω_min × r.
US Curriculum Gaps — Sticking of Person With Wall of Rotor
Topics in this section are in NEET but may be framed differently in US physics courses.Rotor Ride Problem in AP Physics 1
AP Physics 1 covers uniform circular motion and centripetal force but does not include the 'rotor ride' (person sticking to vertical drum wall) as a standard problem type. NRI students need to identify that in this configuration, the centripetal force equation gives N = mω²r, and vertical friction from this normal force must support the person's weight. The rotor problem is a NEET classic combining two concepts (circular motion + friction) that AP Physics tests separately.
- AP Physics 1: centripetal force and friction both covered, but not combined in vertical-axis drum configuration
- NEET: ω_min=√(g/μr) is a direct formula — derive once, memorise, apply in 30 seconds
- Key: horizontal centripetal equation gives N; vertical friction equation gives the condition on ω
Centrifuge and Circular Motion with Friction in University Physics
Halliday & Resnick includes circular motion problems but the rotor-ride-with-friction configuration is not always a standard textbook example. University Physics students learn to apply Newton's law in circular motion but need NEET-specific practice on the rotor problem. The formula ω_min = √(g/μr) requires recognising that the centripetal acceleration provides the effective gravity for the normal force, which is the unusual conceptual element.
- US university: Newton's law in circular motion covered; rotor-ride-friction not always a standard example
- NEET: also tests minimum linear speed v_min=√(gr/μ) and minimum rotational frequency n_min=(1/2π)√(g/μr)
- Practise with r=1m, μ=0.5: ω_min=√(20)≈4.47 rad/s, n_min≈0.71 rev/s, T_max≈1.4 s
NEET-Style Practice — Sticking of Person With Wall of Rotor
4 QuestionsPractice Problems — Sticking of Person With Wall of Rotor
Click "Reveal Answer" after attempting👁 Reveal Answer
👁 Reveal Answer
👁 Reveal Answer
👁 Reveal Answer
Physics — Friction Revision Checklist
Use this section for quick chapter tracking before mocks, part tests, and final NEET revision.
FAQ — Sticking of Person With Wall of Rotor
Notes · Downloads · Revision · Important QuestionsWhat is the formula for minimum angular velocity in the rotor problem?
Why is ω_min independent of mass?
What is the minimum tangential speed for the rotor problem?
How does ω_min change if the radius is quadrupled?
What is the maximum time period for the rotor?
What physical mechanism holds the person up in a rotor?
Can I use v instead of ω in NEET problems?
What if the friction is kinetic in the rotor problem?
NEET NRI Counseling & Admission eBook Download
A practical guide covering sponsor rules, document checklist, verification traps, NRI quota reality, and step-by-step counselling flow. Designed to prevent last-minute rejections and wrong choice filling.
Schedule Trial Session For NEET Prep
Get a short diagnostic + study roadmap: syllabus gaps (NCERT vs U.S. curriculum), weak chapters, and the exact weekly plan needed to improve accuracy under time.