A7LAM CSCA ACADEMYCSCA Academy / Physics / Mechanics
CSCA Physics · Lesson 5 of 16Circular motion and gravitation
Mouvement circulaire et gravitation · الحركة الدائرية والجاذبية
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An object moving in a circle is always accelerating towards the centre. For planets and satellites, gravity provides that centripetal force.
Key ideas
- Uniform circular motion: v = 2πr/T, ω = 2π/T, v = ωr.
- Centripetal acceleration a = v²/r, pointing to the centre.
- Gravitation: F = Gm₁m₂/r², G = 6.67 × 10⁻¹¹ N·m²/kg².
- In orbit, gravity is the centripetal force: GMm/r² = mv²/r.
Formulas to know
- F = mv²/r = mω²r
- Orbital speed v = √(GM/r)
- At the surface: g = GM/R²
Worked example
A 1,000 kg car takes a curve of radius 50 m at 10 m/s. Centripetal force?
- Formula: F = mv²/r
- Replace: F = 1,000 × 10² / 50
- Compute: F = 100,000 / 50
Answer: F = 2,000 N
Practice questions
1. The distance between two masses doubles. The gravitational force becomes:
2 times larger · half · a quarter ✓ · 4 times larger
F ∝ 1/r², (1/2)² = 1/4.
2. A wheel turns once every 0.5 s. Angular speed?
π rad/s · 2π rad/s · 4π rad/s ✓ · 0.5 rad/s
ω = 2π/T = 2π/0.5 = 4π rad/s.
3. Which satellite moves faster?
The one in the higher orbit · The one in the lower orbit ✓ · Both the same · It depends on its mass
v = √(GM/r): smaller r, larger v.