Circular Motion Equations Worksheet
Practice uniform circular motion with 10 problems covering centripetal acceleration, centripetal force, angular velocity, and period. Full solutions included.
View worksheet →Gravitation Equations Worksheet
Practice gravitation with 10 problems on Newton's universal law, field strength, and orbital motion. Includes full worked solutions.
Equations you will need
| F = Gm₁m₂/r² | Newton's law of universal gravitation |
| g = GM/r² | Gravitational field strength |
| v = √(GM/r) | Orbital speed for circular orbit |
| T² = (4π²/GM)r³ | Kepler's 3rd law |
| U = -Gm₁m₂/r | Gravitational potential energy |
Symbol key
| Symbol | Quantity | Unit |
|---|---|---|
| F | force | N |
| G | gravitational constant | 6.67 × 10⁻¹¹ N·m²/kg² |
| m | mass | kg |
| M | central body mass | kg |
| r | separation / orbit radius | m |
| g | field strength | N/kg or m/s² |
| v | orbital speed | m/s |
| T | orbital period | s |
Practice problems
Attempt each problem on paper first, then click Show answer to check your working.
-
Find gravitational force between two 100 kg masses 2 m apart.
Show answer
F = (6.67×10⁻¹¹)(10⁴)/4 = 1.67×10⁻⁷ N -
Find g at Earth's surface. (M=5.97×10²⁴ kg, r=6.37×10⁶ m)
Show answer
g = (6.67×10⁻¹¹)(5.97×10²⁴)/(6.37×10⁶)² = 9.81 m/s² -
Find orbital speed at 7×10⁶ m above Earth's centre.
Show answer
v = √((6.67×10⁻¹¹)(5.97×10²⁴)/7×10⁶) = 7546 m/s -
Find period of a satellite orbiting Earth at radius 8×10⁶ m.
Show answer
v = √(GM/r) = 7058 m/s; T = 2πr/v = 7123 s ≈ 119 min -
Find gravitational PE of a 1000 kg satellite at 4×10⁷ m from Earth's centre.
Show answer
U = -(6.67×10⁻¹¹)(5.97×10²⁴)(1000)/4×10⁷ = -9.95×10⁹ J -
Find g at 2×10⁷ m above Earth's centre (about 3 Earth radii).
Show answer
g = GM/r² = (3.98×10¹⁴)/4×10¹⁴ = 0.995 m/s² -
At what height above Earth's surface is g half its surface value?
Show answer
r₂² = 2r₁² → r₂ = r₁√2 = 9.01×10⁶ m; h = r₂ - 6.37×10⁶ = 2.64×10⁶ m -
Find the mass of the Sun given Earth's orbital radius (1.5×10¹¹ m) and period (3.16×10⁷ s).
Show answer
M = (4π²r³)/(GT²) = 2.0×10³⁰ kg -
Find the escape velocity from Earth's surface.
Show answer
v_esc = √(2GM/r) = √(2 × 3.98×10¹⁴/6.37×10⁶) = 11,200 m/s -
A geostationary satellite has T = 86,400 s. Find its orbital radius.
Show answer
r³ = GMT²/(4π²) = 7.54×10²² → r = 4.23×10⁷ m
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View worksheet →About this worksheet
This gravitation equations worksheet covers the essential equations for mechanics at the A-Level / AP Physics 1 & 2 level. Every problem has been written to mirror the style and difficulty of real exam questions, with full algebraic working shown in the solutions.
If you find these problems too straightforward, try the more advanced worksheets in the same topic listed above. If they feel too difficult, start by reviewing the equation definitions in the box at the top of this page and then return to question 1.