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 worksheet Practise 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

For passenger comfort the centripetal acceleration on a railway curve must not exceed 0.5 m/s². What is the smallest radius r_min for a curve taken at 240 km/h?

v = 240 km/ha_max = 0.5 m/s²

r_min = m

2.Easy

A 1400 kg car drives around a flat curve of radius 200 m at a constant 20 m/s. Find its centripetal acceleration a_c.

m = 1400 kgv = 20 m/sr = 200 m

a_c = m/s²

3.Medium

A road engineer wants cars to take a curve of radius 70 m at 60 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 70 mv = 60 km/hg = 9.81 m/s²

θ = °

4.Medium

A small ball on a string of length 2 m moves in a horizontal circle so that the string makes a constant angle of 40° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the speed v of the ball.

L = 2 mθ = 40°g = 9.81 m/s²

v = m/s

5.Hard

A 3.5 kg cart is released from rest at a height of 15 m on a frictionless track and runs through a vertical loop of radius 3 m. Use g = 9.81 m/s². Find the normal force N_bottom of the track on the cart at the bottom of the loop.

m = 3.5 kgh = 15 mR = 3 mg = 9.81 m/s²

N_bottom = N

6.Hard

A 1.6 kg ball on a light string 0.5 m long is swung in a vertical circle. At the lowest point its speed is 7.5 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension T_top in the string at the highest point.

m = 1.6 kgr = 0.5 mv_bottom = 7.5 m/sg = 9.81 m/s²

T_top = N

Answer key

1. r_min = 8889 m
2. a_c = 2 m/s²
3. θ = 22.02 °
4. v = 3.253 m/s
5. N_bottom = 377.7 N
6. T_top = 101.5 N

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