ScienceAges 16-18

Circular motion & centripetal force

Use F = mv² ÷ r to calculate the inward centripetal force acting on a mass in uniform circular motion. Review suitability for your learners before teaching.

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Worksheet StudioPractice pack · Ages 16-18

Circular motion & centripetal force

Take your time. Show your thinking.

1. A 40 kg mass moves in a horizontal circle of radius 5 m at a constant speed of 10 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
m = 40 kg, r = 5 m → v = 10 m/s → F_c = ? · F_c = mv² ÷ r
2. A 30 kg mass moves in a horizontal circle of radius 6 m at a constant speed of 12 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
m = 30 kg, r = 6 m → v = 12 m/s → F_c = ? · F_c = mv² ÷ r
3. A 10 kg mass moves in a horizontal circle of radius 10 m at a constant speed of 9 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
m = 10 kg, r = 10 m → v = 9 m/s → F_c = ? · F_c = mv² ÷ r
4. A 14 kg mass moves in a horizontal circle of radius 2 m at a constant speed of 8 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
m = 14 kg, r = 2 m → v = 8 m/s → F_c = ? · F_c = mv² ÷ r
5. A 6 kg mass moves in a horizontal circle of radius 2 m at a constant speed of 8 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
m = 6 kg, r = 2 m → v = 8 m/s → F_c = ? · F_c = mv² ÷ r
6. A 10 kg mass moves in a horizontal circle of radius 10 m at a constant speed of 5 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
m = 10 kg, r = 10 m → v = 5 m/s → F_c = ? · F_c = mv² ÷ r
7. A 4 kg mass moves in a horizontal circle of radius 4 m at a constant speed of 7 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
m = 4 kg, r = 4 m → v = 7 m/s → F_c = ? · F_c = mv² ÷ r
8. A 4 kg mass moves in a horizontal circle of radius 2 m at a constant speed of 8 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
m = 4 kg, r = 2 m → v = 8 m/s → F_c = ? · F_c = mv² ÷ r
9. A 48 kg mass moves in a horizontal circle of radius 8 m at a constant speed of 10 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
m = 48 kg, r = 8 m → v = 10 m/s → F_c = ? · F_c = mv² ÷ r
10. A 6 kg mass moves in a horizontal circle of radius 3 m at a constant speed of 3 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
m = 6 kg, r = 3 m → v = 3 m/s → F_c = ? · F_c = mv² ÷ r
11. A 6 kg mass moves in a horizontal circle of radius 6 m at a constant speed of 9 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
m = 6 kg, r = 6 m → v = 9 m/s → F_c = ? · F_c = mv² ÷ r
12. A 20 kg mass moves in a horizontal circle of radius 5 m at a constant speed of 6 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
m = 20 kg, r = 5 m → v = 6 m/s → F_c = ? · F_c = mv² ÷ r

12 questions · Seed 104732 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 16-18

Circular motion & centripetal force

Answers and reasoning. Review before teaching.

1. A 40 kg mass moves in a horizontal circle of radius 5 m at a constant speed of 10 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
800 N
Centripetal force F = (m × v²) ÷ r = (40 × 10²) ÷ 5 = 4000 ÷ 5 = 800 N.
2. A 30 kg mass moves in a horizontal circle of radius 6 m at a constant speed of 12 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
720 N
Centripetal force F = (m × v²) ÷ r = (30 × 12²) ÷ 6 = 4320 ÷ 6 = 720 N.
3. A 10 kg mass moves in a horizontal circle of radius 10 m at a constant speed of 9 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
81 N
Centripetal force F = (m × v²) ÷ r = (10 × 9²) ÷ 10 = 810 ÷ 10 = 81 N.
4. A 14 kg mass moves in a horizontal circle of radius 2 m at a constant speed of 8 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
448 N
Centripetal force F = (m × v²) ÷ r = (14 × 8²) ÷ 2 = 896 ÷ 2 = 448 N.
5. A 6 kg mass moves in a horizontal circle of radius 2 m at a constant speed of 8 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
192 N
Centripetal force F = (m × v²) ÷ r = (6 × 8²) ÷ 2 = 384 ÷ 2 = 192 N.
6. A 10 kg mass moves in a horizontal circle of radius 10 m at a constant speed of 5 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
25 N
Centripetal force F = (m × v²) ÷ r = (10 × 5²) ÷ 10 = 250 ÷ 10 = 25 N.
7. A 4 kg mass moves in a horizontal circle of radius 4 m at a constant speed of 7 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
49 N
Centripetal force F = (m × v²) ÷ r = (4 × 7²) ÷ 4 = 196 ÷ 4 = 49 N.
8. A 4 kg mass moves in a horizontal circle of radius 2 m at a constant speed of 8 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
128 N
Centripetal force F = (m × v²) ÷ r = (4 × 8²) ÷ 2 = 256 ÷ 2 = 128 N.
9. A 48 kg mass moves in a horizontal circle of radius 8 m at a constant speed of 10 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
600 N
Centripetal force F = (m × v²) ÷ r = (48 × 10²) ÷ 8 = 4800 ÷ 8 = 600 N.
10. A 6 kg mass moves in a horizontal circle of radius 3 m at a constant speed of 3 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
18 N
Centripetal force F = (m × v²) ÷ r = (6 × 3²) ÷ 3 = 54 ÷ 3 = 18 N.
11. A 6 kg mass moves in a horizontal circle of radius 6 m at a constant speed of 9 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
81 N
Centripetal force F = (m × v²) ÷ r = (6 × 9²) ÷ 6 = 486 ÷ 6 = 81 N.
12. A 20 kg mass moves in a horizontal circle of radius 5 m at a constant speed of 6 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
144 N
Centripetal force F = (m × v²) ÷ r = (20 × 6²) ÷ 5 = 720 ÷ 5 = 144 N.

12 questions · Seed 104732 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Circular motion & centripetal force

Take your time. Show your thinking.

1. A 40 kg mass moves in a horizontal circle of radius 5 m at a constant speed of 10 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
m = 40 kg, r = 5 m → v = 10 m/s → F_c = ? · F_c = mv² ÷ r
2. A 30 kg mass moves in a horizontal circle of radius 6 m at a constant speed of 12 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
m = 30 kg, r = 6 m → v = 12 m/s → F_c = ? · F_c = mv² ÷ r
3. A 10 kg mass moves in a horizontal circle of radius 10 m at a constant speed of 9 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
m = 10 kg, r = 10 m → v = 9 m/s → F_c = ? · F_c = mv² ÷ r
4. A 14 kg mass moves in a horizontal circle of radius 2 m at a constant speed of 8 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
m = 14 kg, r = 2 m → v = 8 m/s → F_c = ? · F_c = mv² ÷ r
5. A 6 kg mass moves in a horizontal circle of radius 2 m at a constant speed of 8 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
m = 6 kg, r = 2 m → v = 8 m/s → F_c = ? · F_c = mv² ÷ r
6. A 10 kg mass moves in a horizontal circle of radius 10 m at a constant speed of 5 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
m = 10 kg, r = 10 m → v = 5 m/s → F_c = ? · F_c = mv² ÷ r
7. A 4 kg mass moves in a horizontal circle of radius 4 m at a constant speed of 7 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
m = 4 kg, r = 4 m → v = 7 m/s → F_c = ? · F_c = mv² ÷ r
8. A 4 kg mass moves in a horizontal circle of radius 2 m at a constant speed of 8 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
m = 4 kg, r = 2 m → v = 8 m/s → F_c = ? · F_c = mv² ÷ r
9. A 48 kg mass moves in a horizontal circle of radius 8 m at a constant speed of 10 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
m = 48 kg, r = 8 m → v = 10 m/s → F_c = ? · F_c = mv² ÷ r
10. A 6 kg mass moves in a horizontal circle of radius 3 m at a constant speed of 3 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
m = 6 kg, r = 3 m → v = 3 m/s → F_c = ? · F_c = mv² ÷ r
11. A 6 kg mass moves in a horizontal circle of radius 6 m at a constant speed of 9 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
m = 6 kg, r = 6 m → v = 9 m/s → F_c = ? · F_c = mv² ÷ r
12. A 20 kg mass moves in a horizontal circle of radius 5 m at a constant speed of 6 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
m = 20 kg, r = 5 m → v = 6 m/s → F_c = ? · F_c = mv² ÷ r

12 questions · Seed 104732 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Circular motion & centripetal force

Answers and reasoning. Review before teaching.

1. A 40 kg mass moves in a horizontal circle of radius 5 m at a constant speed of 10 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
800 N
Centripetal force F = (m × v²) ÷ r = (40 × 10²) ÷ 5 = 4000 ÷ 5 = 800 N.
2. A 30 kg mass moves in a horizontal circle of radius 6 m at a constant speed of 12 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
720 N
Centripetal force F = (m × v²) ÷ r = (30 × 12²) ÷ 6 = 4320 ÷ 6 = 720 N.
3. A 10 kg mass moves in a horizontal circle of radius 10 m at a constant speed of 9 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
81 N
Centripetal force F = (m × v²) ÷ r = (10 × 9²) ÷ 10 = 810 ÷ 10 = 81 N.
4. A 14 kg mass moves in a horizontal circle of radius 2 m at a constant speed of 8 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
448 N
Centripetal force F = (m × v²) ÷ r = (14 × 8²) ÷ 2 = 896 ÷ 2 = 448 N.
5. A 6 kg mass moves in a horizontal circle of radius 2 m at a constant speed of 8 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
192 N
Centripetal force F = (m × v²) ÷ r = (6 × 8²) ÷ 2 = 384 ÷ 2 = 192 N.
6. A 10 kg mass moves in a horizontal circle of radius 10 m at a constant speed of 5 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
25 N
Centripetal force F = (m × v²) ÷ r = (10 × 5²) ÷ 10 = 250 ÷ 10 = 25 N.
7. A 4 kg mass moves in a horizontal circle of radius 4 m at a constant speed of 7 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
49 N
Centripetal force F = (m × v²) ÷ r = (4 × 7²) ÷ 4 = 196 ÷ 4 = 49 N.
8. A 4 kg mass moves in a horizontal circle of radius 2 m at a constant speed of 8 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
128 N
Centripetal force F = (m × v²) ÷ r = (4 × 8²) ÷ 2 = 256 ÷ 2 = 128 N.
9. A 48 kg mass moves in a horizontal circle of radius 8 m at a constant speed of 10 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
600 N
Centripetal force F = (m × v²) ÷ r = (48 × 10²) ÷ 8 = 4800 ÷ 8 = 600 N.
10. A 6 kg mass moves in a horizontal circle of radius 3 m at a constant speed of 3 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
18 N
Centripetal force F = (m × v²) ÷ r = (6 × 3²) ÷ 3 = 54 ÷ 3 = 18 N.
11. A 6 kg mass moves in a horizontal circle of radius 6 m at a constant speed of 9 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
81 N
Centripetal force F = (m × v²) ÷ r = (6 × 9²) ÷ 6 = 486 ÷ 6 = 81 N.
12. A 20 kg mass moves in a horizontal circle of radius 5 m at a constant speed of 6 m/s. Using F = mv² ÷ r, calculate the centripetal force acting toward the centre.
144 N
Centripetal force F = (m × v²) ÷ r = (20 × 6²) ÷ 5 = 720 ÷ 5 = 144 N.

12 questions · Seed 104732 · Age guidance, not curriculum certification