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Centripetal Force worksheet

Grades 11–12 · CCSS HSA.CED.A.4

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Solve for: Speed
- Describe the motion with: Linear speed (v)
- Centripetal force (F): 12,000 N
- Mass (m): 1,500 kg
- Radius of the circle (r): 42 m
- Show speed in: Miles per hour (mph)
Find: Speed
Answer
2.
Problem 2.
- Solve for: Force
- Describe the motion with: Linear speed (v)
- Mass (m): 1,175 kg
- Speed along the circle (v): 18 m/s
- Radius of the circle (r): 45 m
- Show force in: Newtons (N)
Find: Centripetal force
Answer
3.
Problem 3.
- Solve for: Radius
- Describe the motion with: Linear speed (v)
- Centripetal force (F): 12,250 N
- Mass (m): 1,100 kg
- Speed along the circle (v): 18 m/s
- Show radius in: Inches (in)
Find: Radius
Answer
4.
Problem 4.
- Solve for: Force
- Describe the motion with: Linear speed (v)
- Mass (m): 1,300 kg
- Speed along the circle (v): 20 m/s
- Radius of the circle (r): 70 m
- Show force in: Newtons (N)
Find: Centripetal force
Answer
5.
Problem 5.
- Solve for: Radius
- Describe the motion with: Angular velocity (ω)
- Centripetal force (F): 9,000 N
- Mass (m): 1,500 kg
- Angular velocity (ω): 0.4 rad/s
- Show radius in: Meters (m)
Find: Radius
Answer
6.
Problem 6.
- Solve for: Force
- Describe the motion with: Linear speed (v)
- Mass (m): 1,150 kg
- Speed along the circle (v): 20 m/s
- Radius of the circle (r): 38 m
- Show force in: Newtons (N)
Find: Centripetal force
Answer
7.
Problem 7.
- Solve for: Mass
- Describe the motion with: Linear speed (v)
- Centripetal force (F): 8,000 N
- Speed along the circle (v): 16 m/s
- Radius of the circle (r): 44 m
- Show mass in: Pounds (lb)
Find: Mass
Answer
8.
Problem 8.
- Solve for: Radius
- Describe the motion with: Linear speed (v)
- Centripetal force (F): 10,750 N
- Mass (m): 1,100 kg
- Speed along the circle (v): 18 m/s
- Show radius in: Miles (mi)
Find: Radius
Answer
9.
Problem 9.
- Solve for: Radius
- Describe the motion with: Angular velocity (ω)
- Centripetal force (F): 7,000 N
- Mass (m): 1,200 kg
- Angular velocity (ω): 0.5 rad/s
- Show radius in: Centimeters (cm)
Find: Radius
Answer
10.
Problem 10.
- Solve for: Mass
- Describe the motion with: Linear speed (v)
- Centripetal force (F): 12,250 N
- Speed along the circle (v): 13 m/s
- Radius of the circle (r): 38 m
- Show mass in: Kilograms (kg)
Find: Mass
Answer

Answer key: Centripetal Force worksheet

1. Speed: 41 mph
1. Find the speed by turning F = m × v² ÷ r around: the square root of force × radius ÷ mass
  $\sqrt{\frac{12,000 \times 42}{1,500}}$ $= 18.330303 m/s$
2. Change the answer to mph, the unit you picked: divide by 0.44704
  $\frac{18.330303}{0.44704}$ $= 41.00372 mph$
3. Find the inward acceleration: force ÷ mass (the same as speed squared ÷ radius)
  $\frac{12,000}{1,500}$ $= 8 m/s²$
2. Centripetal force: 8,460 N
1. Find the inward force: mass × speed squared ÷ radius. Speed is squared, so it matters most
  $\frac{1,175 \times 18^{2}}{45}$ $= 8,460 N$
2. Find the inward acceleration: force ÷ mass (the same as speed squared ÷ radius)
  $\frac{8,460}{1,175}$ $= 7.2 m/s²$
3. Radius: 1,145.43 in
1. Find the radius by turning F = m × v² ÷ r around: mass × speed squared ÷ force
  $\frac{1,100 \times 18^{2}}{12,250}$ $= 29.093878 m$
2. Change the answer to in, the unit you picked: divide by 0.0254
  $\frac{29.093878}{0.0254}$ $= 1,145.42825 in$
3. Find the inward acceleration: force ÷ mass (the same as speed squared ÷ radius)
  $\frac{12,250}{1,100}$ $= 11.136364 m/s²$
4. Centripetal force: 7,428.57 N
1. Find the inward force: mass × speed squared ÷ radius. Speed is squared, so it matters most
  $\frac{1,300 \times 20^{2}}{70}$ $= 7,428.571429 N$
2. Find the inward acceleration: force ÷ mass (the same as speed squared ÷ radius)
  $\frac{7,428.571429}{1,300}$ $= 5.714286 m/s²$
5. Radius: 37.5 m
1. Find the radius by turning F = m × ω² × r around: force ÷ (mass × angular velocity squared)
  $\frac{9,000}{1,500 \times {0.4}^{2}}$ $= 37.5 m$
2. Find the inward acceleration: force ÷ mass (the same as speed squared ÷ radius)
  $\frac{9,000}{1,500}$ $= 6 m/s²$
6. Centripetal force: 12,105.26 N
1. Find the inward force: mass × speed squared ÷ radius. Speed is squared, so it matters most
  $\frac{1,150 \times 20^{2}}{38}$ $= 12,105.263158 N$
2. Find the inward acceleration: force ÷ mass (the same as speed squared ÷ radius)
  $\frac{12,105.263158}{1,150}$ $= 10.526316 m/s²$
7. Mass: 3,031.36 lb
1. Find the mass by turning F = m × v² ÷ r around: force × radius ÷ speed squared
  $\frac{8,000 \times 44}{16^{2}}$ $= 1,375 kg$
2. Change the answer to lb, the unit you picked: divide by 0.45359237
  $\frac{1,375}{0.45359237}$ $= 3,031.356105 lb$
3. Find the inward acceleration: force ÷ mass (the same as speed squared ÷ radius)
  $\frac{8,000}{1,375}$ $= 5.818182 m/s²$
8. Radius: 0.02 mi
1. Find the radius by turning F = m × v² ÷ r around: mass × speed squared ÷ force
  $\frac{1,100 \times 18^{2}}{10,750}$ $= 33.153488 m$
2. Change the answer to mi, the unit you picked: divide by 1,609.344
  $\frac{33.153488}{1,609.344}$ $= 0.020601 mi$
3. Find the inward acceleration: force ÷ mass (the same as speed squared ÷ radius)
  $\frac{10,750}{1,100}$ $= 9.772727 m/s²$
9. Radius: 2,333.33 cm
1. Find the radius by turning F = m × ω² × r around: force ÷ (mass × angular velocity squared)
  $\frac{7,000}{1,200 \times {0.5}^{2}}$ $= 23.333333 m$
2. Change the answer to cm, the unit you picked: divide by 0.01
  $\frac{23.333333}{0.01}$ $= 2,333.333333 cm$
3. Find the inward acceleration: force ÷ mass (the same as speed squared ÷ radius)
  $\frac{7,000}{1,200}$ $= 5.833333 m/s²$
10. Mass: 2,754.44 kg
1. Find the mass by turning F = m × v² ÷ r around: force × radius ÷ speed squared
  $\frac{12,250 \times 38}{13^{2}}$ $= 2,754.43787 kg$
2. Find the inward acceleration: force ÷ mass (the same as speed squared ÷ radius)
  $\frac{12,250}{2,754.43787}$ $= 4.447368 m/s²$