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 →Newton's Laws Equations Worksheet
Master Newton's three laws of motion with 10 problems covering net force, weight, friction, and tension. Each problem includes a full worked solution.
Equations you will need
| F = ma | Newton's 2nd law: net force = mass × acceleration |
| W = mg | Weight: mass × gravitational field strength |
| f = μN | Friction: coefficient × normal force |
| ΣF = 0 | Newton's 1st law (equilibrium) |
| F₁₂ = -F₂₁ | Newton's 3rd law (equal and opposite) |
Symbol key
| Symbol | Quantity | Unit |
|---|---|---|
| F | force | N (newtons) |
| m | mass | kg |
| a | acceleration | m/s² |
| W | weight | N |
| g | gravitational field strength | 9.8 m/s² (Earth) |
| μ | coefficient of friction | dimensionless |
| N | normal force | N |
Practice problems
Attempt each problem on paper first, then click Show answer to check your working.
-
A 5 kg box is pushed with a horizontal force of 20 N on a frictionless surface. Find the acceleration.
Show answer
a = F/m = 20/5 = 4 m/s² -
Find the weight of a 70 kg person on Earth. (g = 9.8 m/s²)
Show answer
W = mg = 70 × 9.8 = 686 N -
A 2 kg object accelerates at 3 m/s² across a rough surface. The applied force is 10 N. Find the friction force.
Show answer
F_net = ma → 10 - f = 2(3) → f = 4 N -
A 10 kg block sits on a surface with μ = 0.3. Find the friction force needed to start moving it. (g = 9.8 m/s²)
Show answer
N = mg = 98 N; f = μN = 0.3(98) = 29.4 N -
Two forces act on a 4 kg object: 12 N right and 8 N left. Find the acceleration.
Show answer
F_net = 12 - 8 = 4 N; a = 4/4 = 1 m/s² -
A car of mass 1200 kg decelerates from 20 m/s to rest in 5 s. Find the braking force.
Show answer
a = -4 m/s²; F = ma = 1200(-4) = -4800 N (4800 N opposing motion) -
A 3 kg mass hangs from a rope. Find the tension when it is stationary. (g = 9.8 m/s²)
Show answer
T = mg = 3(9.8) = 29.4 N -
Same 3 kg mass now accelerates upward at 2 m/s². Find the new tension.
Show answer
T - mg = ma → T = m(g + a) = 3(11.8) = 35.4 N -
A 50 kg sled is pulled by a 200 N force on ice (μ = 0.1). Find acceleration. (g = 9.8 m/s²)
Show answer
f = 0.1(50)(9.8) = 49 N; F_net = 151 N; a = 3.02 m/s² -
An 80 kg astronaut pushes off a 200 kg satellite with a force of 100 N for 0.5 s. Find each one's acceleration.
Show answer
a_astronaut = 100/80 = 1.25 m/s²; a_satellite = 100/200 = 0.5 m/s² (opposite direction)
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View worksheet →About this worksheet
This newton's laws equations worksheet covers the essential equations for mechanics at the GCSE / AP Physics 1 / IB SL 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.