JEE/NEET Physics · Rotational Motion series · Part 6 of 8 · All parts →
- Rolling = moving forward while spinning, perfectly matched: forward speed = R × spin rate
- Rolling energy always has two parts: forward energy + spin energy
- The shape, not the weight, decides the race: sphere beats disc beats ring
- Ramp acceleration: a = g·sinθ ÷ (1 + shape number)
- A skidding sphere launched without spin ends at 5/7 of its speed — whatever the friction
Release a marble (solid sphere), a coin (disc), and a ring together at the top of a ramp. Same ramp, any sizes. They arrive in a fixed order — marble first, coin second, ring last. Every time. Not weight, not size — pure shape. Rolling is translation + spin happening to one body, and Part 6 of the Rotational Motion series assembles the whole machine.
- What rolling really is
- The no-slip handshake
- Rolling energy: always two parts
- The great race, explained
- Skidding to gripping: the 5/7 story
- Solved examples
- Common mistakes
- This physics in your daily life
- Practice set
- Recap
What Rolling Really Is
Watch the point of a rolling wheel touching the road: at that instant it is perfectly still — the wheel pivots on its contact point like a door on a hinge. The wheel’s centre moves at speed v; the wheel’s top moves at 2v; the bottom at 0. That’s pure rolling.
The No-Slip Handshake
This one handshake ties the two motions together: the centre’s forward speed is locked to the spin. Everything in rolling problems flows from it.
Rolling Energy: Always Two Parts
A rolling body’s energy splits between going forward and spinning — the split decided purely by shape. A ring spends HALF its energy spinning; a sphere only 29%. More spin-tax = slower arrival. That’s the whole race.
The Great Race, Explained
Rolling down a ramp of height h: gravity’s energy Mgh pays for forward + spin energy. Rearranged: v² = 2gh ÷ (1 + shape number) — and mass and radius have cancelled completely. Only shape remains:
| Racer | Shape number | Speed after 1.7 m drop | Finish |
|---|---|---|---|
| Marble (solid sphere) | 0.40 | 4.93 m/s | 1st — least spin-tax |
| Coin (disc) | 0.50 | 4.76 m/s | 2nd |
| Ring | 1.00 | 4.12 m/s | 3rd — half its energy goes to spin |
(A frictionless sliding block would do 5.83 m/s — every roller pays a shape tax; the sphere pays least.)
Skidding to Gripping: The 5/7 Story
Launch a solid sphere along rough ground fast, with zero spin. Initially it skids (bottom sliding). Friction then does two jobs at once: slows the forward motion AND spins the sphere up — until the handshake v = Rω locks in. The remarkable result: the final rolling speed is exactly 5/7 of the launch speed — no matter how strong the friction is (friction only decides how long the skid lasts). JEE loves this number.
Solved Examples
Forward: ½ × 2 × 16 = 16 J. Spin: ¼Mv² = 8 J (a disc always sends 1/3 of its energy to spin).
Total 24 J. ✔
Answer: 24 J (16 forward + 8 spin)
Apply v = √(2gh ÷ (1 + shape number)): sphere √(34/1.4) = 4.93; disc √(34/1.5) = 4.76; ring √(34/2) = 4.12 m/s.
Check: same order as the table — shape only. ✔
Answer: 4.93 > 4.76 > 4.12 m/s
During skid: friction pushes back (slowing forward motion) and turns the sphere up from zero spin — until v = Rω.
The counting: forward momentum drops as M(v − 10), spin quantity grows as (2/5)MR·v… setting v = Rω at the end gives the clean result:
v_final = (5/7) × 10 ≈ 7.14 m/s — independent of friction strength. ✔
Answer: (5/7) × 10 ≈ 7.14 m/s, whatever the friction
- Writing only ½Mv² for a rolling body. The spin energy is never optional in rolling — forgetting it erases the entire shape story.
- ‘Friction always slows things.’ For the launched sphere, friction spins it up (increasing spin energy) while slowing it. Friction opposes sliding at the contact, not motion in general.
- Believing heavier or bigger rolls faster. The race formula contains only shape — a marble beats a giant ring down the same ramp.
- Using v = Rω during skidding. The handshake holds only once pure rolling begins.
- Energy conservation with skidding friction present. Skidding friction wastes energy as heat — account for it or use the momentum-counting route.
This Physics in Your Daily Life
- ABS brakes in every modern car exist to preserve rolling: a locked, skidding wheel loses steering and grip. The system pulses the brakes to keep the no-slip handshake alive.
- Railways beat roads on efficiency: steel wheel on steel rail has ~1/10 the rolling resistance of rubber on asphalt — the shape-tax insight, industrialised.
- Spin bowling in cricket: a ball that grips the pitch converts forward speed to spin — the post-grip speed change is the 5/7-type physics, weaponised.
- Cycle wheels are spoked, not solid discs: spokes give stiffness with less laziness per kilogram — easier acceleration.
- Landing rovers on the Moon or Mars pass through the skid-to-grip phase when wheels touch regolith — engineers model exactly this card.
Practice set (answers hidden — try first)
(NEET-level) A rolling ring: fraction of energy that is spin:
(JEE Main-level) Solid sphere down a 30° ramp. Acceleration (g = 10):
(Concept) Equal-mass disc and ring at equal speed — which has more total energy?
(NEET-level) A wheel rolls at v. Its topmost point moves at:
(JEE Main-level) A sphere launches at 7 m/s, no spin. Final rolling speed:
- 🧠 Race chant: ‘sphere, disc, ring — 7, 6.7, 5’ (ramp accelerations in units of g·sinθ × 0.1) — shape number 0.4, 0.5, 1.0.
- 🧠 Handshake: v = Rω; bottom still, centre v, top 2v — ‘pivot on the contact point’.
- 🧠 The 5/7 number: launched sphere, no spin → final speed 5/7 of launch, friction irrelevant.
- 🏠 Daily: ABS brakes exist to preserve rolling — a skidding wheel loses grip AND steering.
- 🏠 Daily: trains beat trucks on efficiency — steel-on-steel rolling wastes ~1/10 of rubber-on-road.
- rolling = forward + spin, handshaken: v = Rω; bottom point still, top at 2v
- rolling energy = ½Mv² × (1 + shape number): sphere 1.4, disc 1.5, ring 2.0
- the race: v = √(2gh/(1 + shape number)) — mass and size cancel; sphere > disc > ring
- friction in rolling re-routes energy, doesn’t always waste it
- launched sphere, no spin: final rolling speed = 5/7 of launch, friction-independent
Quick revision
- Rolling = moving forward while spinning, perfectly matched: forward speed = R × spin rate
- Rolling energy always has two parts: forward energy + spin energy
- The shape, not the weight, decides the race: sphere beats disc beats ring
- Ramp acceleration: a = g·sinθ ÷ (1 + shape number)
- A skidding sphere launched without spin ends at 5/7 of its speed — whatever the friction
- Rolling energy: always two parts
- 1Centre of Mass: The Point That Behaves Like a Particle
- 2Torque: Why Doorknobs Live Far From Hinges
- 3Moment of Inertia: Rotational Mass, and Why Distribution Beats Size
- 4Torque Equals I-Alpha: Newton’s Second Law, Spun
- 5Angular Momentum in Rotation: Conservation Unleashed
- 6Rolling Motion: Translation and Rotation in One Body
- 7Rotational Energy and Flywheels: Spin as a Battery
- 8Equilibrium and Toppling: Why Cranes Don’t Fall Over
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