Gravitation Equations Worksheet
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View worksheet →Circular Motion Equations Worksheet
Practice uniform circular motion with 10 problems covering centripetal acceleration, centripetal force, angular velocity, and period. Full solutions included.
Equations you will need
| a = v²/r | Centripetal acceleration |
| F = mv²/r | Centripetal force |
| ω = v/r | Angular velocity |
| T = 2π/ω | Period |
| v = 2πr/T | Linear speed from radius and period |
Symbol key
| Symbol | Quantity | Unit |
|---|---|---|
| a | centripetal acceleration | m/s² |
| v | linear speed | m/s |
| r | radius | m |
| F | centripetal force | N |
| ω | angular velocity | rad/s |
| T | period | s |
| m | mass | kg |
Practice problems
Attempt each problem on paper first, then click Show answer to check your working.
-
A car travels at 10 m/s on a circular track of radius 20 m. Find centripetal acceleration.
Show answer
a = v²/r = 100/20 = 5 m/s² -
Find the centripetal force on a 1500 kg car going 25 m/s around a 50 m radius curve.
Show answer
F = mv²/r = 1500(625)/50 = 18,750 N -
A point on a 0.3 m diameter wheel rotates at 4 rev/s. Find linear speed.
Show answer
v = 2πr × f = 2π(0.15)(4) = 3.77 m/s -
Find the period of a satellite in a 7000 km orbit moving at 7500 m/s.
Show answer
T = 2πr/v = 2π(7×10⁶)/7500 = 5864 s ≈ 98 min -
A 0.5 kg ball on a 1 m string is whirled at 3 rev/s. Find the tension.
Show answer
ω = 6π rad/s; v = 6π m/s; F = mv²/r = 0.5(6π)²/1 = 177.6 N -
A 800 kg car rounds a flat curve of radius 40 m at 15 m/s. Find required friction force.
Show answer
F = 800(225)/40 = 4500 N -
Find ω for an object completing one revolution every 4 seconds.
Show answer
ω = 2π/T = 2π/4 = 1.57 rad/s -
A 2 kg mass swings in a horizontal circle of radius 0.8 m at angular velocity 5 rad/s. Find centripetal force.
Show answer
v = ωr = 4 m/s; F = mv²/r = 2(16)/0.8 = 40 N -
A car at 20 m/s rounds a curve where max friction force = 8000 N. Min radius if car mass is 1200 kg?
Show answer
8000 = 1200(400)/r → r = 60 m -
The Moon orbits Earth in 27.3 days at radius 3.84×10⁸ m. Find its orbital speed.
Show answer
T = 27.3 × 86400 = 2.36×10⁶ s; v = 2πr/T = 1023 m/s
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View worksheet →About this worksheet
This circular motion equations worksheet covers the essential equations for mechanics at the A-Level / AP Physics 1 / IB HL 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.