Circular and rotational motion in NET is mostly linear mechanics with new symbols: θ for distance, ω for velocity, I for mass, τ for force and L for momentum. Learn that mapping, the centripetal force formula and conservation of angular momentum, and you can handle almost every question this chapter produces.
Key facts
- Physics is 30% of NET-Engineering, a derived 60 of the 200 MCQs.
- Our syllabus data estimates about 6 questions from this chapter.
- Syllabus: angular kinematics, centripetal force, torque, angular momentum, artificial satellites and rotational dynamics.
Source: NUST NET-Engineering composition and the SailToNUST physics syllabus, checked October 2026
What the chapter covers
The chapter opens with angular displacement, velocity and acceleration, then moves to centripetal force. After that it covers moment of inertia, torque and angular momentum, then rolling bodies, and ends with satellites and orbits. NET questions lean on three things: centripetal acceleration numericals, angular momentum conservation, and short satellite facts.
The linear to rotational map
| Linear | Rotational | Link |
|---|---|---|
| displacement s (m) | angle θ (rad) | s = rθ |
| velocity v (m/s) | angular velocity ω (rad/s) | v = rω |
| acceleration a | angular acceleration α | a_t = rα |
| mass m | moment of inertia I (kg m²) | I = Σmr² |
| force F | torque τ (N m) | τ = rF sinθ |
| momentum p = mv | angular momentum L = Iω | L = mvr for a point mass |
| F = ma | τ = Iα | |
| KE = ½mv² | KE = ½Iω² |
If you remember this table, you can rebuild every equation in the chapter from the linear one you already know.
Formulas you need
ω = 2π / T = 2πf rad s⁻¹
rev/min to rad/s: multiply by 2π/60
Centripetal acceleration a_c = v²/r = rω² m s⁻²
Centripetal force F_c = mv²/r = mrω² N
Moments of inertia (axis through centre)
ring / hoop I = MR²
disc I = ½MR²
solid sphere I = ⅖MR²
rod (centre) I = ML²/12
Conservation of angular momentum I₁ω₁ = I₂ω₂
Rolling down a slope from height h (starting at rest)
v = √(2gh / (1 + I/MR²))
hoop: v = √(gh) disc: v = √(4gh/3) sphere: v = √(10gh/7)
Orbital speed v = √(GM/r); near Earth's surface √(gR) ≈ 7.9 km s⁻¹
Geostationary satellite period 24 h, about 36,000 km above the equator
Worked MCQs
1. Wheel turning once a second. A cycle wheel of radius 0.4 m completes one revolution every second. What is the centripetal acceleration of a point on its rim?
(a) 0.4π m/s² (b) 0.8π m/s² (c) 0.4π² m/s² (d) 1.6π² m/s²
ω = 2π / T = 2π rad/s
a = rω² = 0.4 × 4π² = 1.6π² m/s² (about 15.8 m/s²)
Answer (d). Option (b) is the rim speed v = rω = 0.8π m/s, not the acceleration.
2. Halving the radius at fixed ω. A particle moves in a circle at constant angular velocity with angular momentum L. The radius is halved while ω stays the same. What is the new angular momentum?
(a) L/4 (b) L/2 (c) L (d) 2L
L = mvr = m(rω)r = mr²ω
r → r/2 so L → L/4
Answer (a). The common wrong answer is L/2, from treating v as fixed. Here ω is fixed, so v halves too.
3. Energy in a spinning wheel. A heavy wheel with I = 2 kg m² spins at 300 rev/min. What is its rotational kinetic energy?
(a) 100 J (b) 300 J (c) 987 J (d) 9000 J
ω = 300 × 2π / 60 = 10π rad/s
KE = ½Iω² = ½ × 2 × (10π)² = 100π² ≈ 987 J
Answer (c). If you leave ω in rev/min you get 90,000 J. If you convert to rev/s but forget 2π you get 25 J. Both make good distractors, so expect to see one of them in the options.
4. Disc versus hoop on a slope. A disc and a hoop of the same mass and radius roll from rest down a slope of vertical height 1.8 m. With g = 10 m/s², what is the disc's speed at the bottom, and which reaches the bottom first?
disc: v = √(4gh/3) = √(4 × 10 × 1.8 / 3) = √24 ≈ 4.9 m/s
hoop: v = √(gh) = √18 ≈ 4.2 m/s
The disc arrives first at about 4.9 m/s. The hoop puts more of its energy into spinning because all its mass sits at the rim. Mass and radius cancel out, so a small disc beats a big hoop every time.
5. Car on a flat bend. A 1000 kg car takes a flat bend of radius 50 m at 20 m/s. What sideways friction force must the road provide?
(a) 400 N (b) 4000 N (c) 8000 N (d) 20,000 N
F = mv²/r = 1000 × 400 / 50 = 8000 N
Answer (c). Double the speed and the force goes up four times. That is why speed limits on bends matter more than on straights.
Traps that cost marks
- Centripetal force is not a new force. It is whatever supplies the inward pull: tension, friction, gravity or the normal force. It does no work, because it is always perpendicular to the velocity.
- A stone released from a whirl moves along the tangent. It does not fly radially outward.
- Spinning skater. When she pulls her arms in, I drops and ω rises so that Iω stays constant. Her kinetic energy goes up, because KE = L²/2I and I got smaller. The extra energy comes from the work her muscles do.
- Speed in an elliptical orbit. Angular momentum is conserved, so the planet moves fastest at the point closest to the Sun.
- Weightlessness in orbit. Astronauts are not beyond gravity. They and their spacecraft fall together, so the floor pushes on them with zero force.
- Units. Angular momentum is in J s or kg m² s⁻¹. The practice bank has "J s is the unit of" with angular momentum as the answer.
Speed tips for the exam
Convert rev/min with ×π/30. 60 rpm is 2π rad/s, 300 rpm is 10π rad/s, 600 rpm is 20π rad/s.
For ratio questions, write the formula with the fixed quantity explicit. "Same ω" means use L = mr²ω. "Same speed" means use L = mvr. Picking the wrong form is the only real way to miss these.
For orbit questions, remember orbital speed is set by the radius of the orbit and the mass of the planet, not the mass of the satellite. Two satellites at the same height move at the same speed, whatever they weigh.
The energy side of satellites, escape velocity and absolute PE, sits in work, energy and power. For the whole physics paper plan, see the NET physics guide.
FAQ
Do I need to memorise moments of inertia for NET?
Memorise ring, disc, solid sphere and rod about its centre. Those four cover nearly every rolling and spinning-wheel question.
What is the difference between centripetal and centrifugal force?
Centripetal force is the real inward force that keeps a body on a circle. Centrifugal force is the outward pseudo-force you only need inside a rotating frame. In NET answers, the real force is centripetal.
What is the height of a geostationary satellite?
About 36,000 km above the equator, with a period of 24 hours, so it stays over the same point on Earth.
Is rotational motion hard in NET?
The concepts are harder than the arithmetic. Most questions are ratio questions that take under a minute once you know which quantity is held fixed.
