Circular motion worksheet with answers

Free printable Circular motion worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
r = 140 m18 m/sF = ?

A 900 kg car drives around a flat curve of radius 140 m at a constant 18 m/s. Find the inward (centripetal) force Fc needed.

m = 900 kgv = 18 m/sr = 140 m
Fc = N
2.Easy
r = 20 m15 m/sF = ?

A 900 kg car drives around a flat curve of radius 20 m at a constant 15 m/s. Find the inward (centripetal) force Fc needed.

m = 900 kgv = 15 m/sr = 20 m
Fc = N
3.Medium
θ = ?to centre60 km/h

A road engineer wants cars to take a curve of radius 370 m at 60 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 370 mv = 60 km/hg = 9.81 m/s²
θ = °
4.Medium
L = 1.3 m30°

A small ball on a string of length 1.3 m moves in a horizontal circle so that the string makes a constant angle of 30° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 1.3 mθ = 30°g = 9.81 m/s²
T = s
5.Hard
r = 0.7 m9.5 m/svtop​ = ?

A 1 kg ball on a light string 0.7 m long is swung in a vertical circle. At the lowest point its speed is 9.5 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 1 kgr = 0.7 mvbottom = 9.5 m/sg = 9.81 m/s²
Ttop = N
6.Hard
θ = 25°to centrevmax​ = ?

A curve of radius 80 m is banked at 25°, and the coefficient of static friction between tyres and road is 0.1. Use g = 9.81 m/s². Find the highest speed vmax at which a car can take the curve without sliding up and out.

r = 80 mθ = 25°μs = 0.1g = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. Fc = 2083 N
  2. 2. Fc = 10125 N
  3. 3. θ = 4.376 °
  4. 4. T = 2.129 s
  5. 5. Ttop = 79.88 N
  6. 6. vmax = 21.59 m/s

Full step-by-step solutions: practise this topic on examproblems.com.