The **centripetal force equation**, given by F_{c} = (m × v^{2}) ÷ r, is used to calculate the force required to keep an object moving in a circular path. In this equation, F_{c} represents the centripetal force, m is the mass of the object, v denotes the velocity of the object, and r signifies the radius of the circular path.

## Practice problems

### Problem #1

Determine the centripetal force acting on a car of mass 1000 kg as it moves in a circular path with a velocity of 1.8 km/h. The radius of the circular path is 10 m.

**Solution**

Given data:

- Centripetal force acting on a car, F
_{c}= ? - Mass of a car, m = 1000 kg
- Velocity of a car, v = 1.8 km/h = 0.5 m/s
- Radius of a circular path, r = 10 m

Applying the formula:

- F
_{c}= (m × v^{2}) ÷ r - F
_{c}= [1000 × (0.5)^{2}] ÷ 10 - F
_{c}= 250 ÷ 10 - F
_{c}= 25 N

Therefore, the centripetal force acting on a car is **25 N**.

### Problem #2

Find the centripetal force acting on a boy of mass 30 kg who is enjoying a merry-go-round ride. The boy sits on a merry-go-round rotating in a circular path with a radius of 6 m and a velocity of 2 m/s.

**Solution**

Given data:

- Centripetal force acting on a boy, F
_{c}= ? - Mass of a boy, m = 30 kg
- Radius of a circular path, r = 6 m
- Velocity of a boy, v = 2 m/s

Applying the formula:

- F
_{c}= (m × v^{2}) ÷ r - F
_{c}= [30 × (2)^{2}] ÷ 6 - F
_{c}= 120 ÷ 6 - F
_{c}= 20 N

Therefore, the centripetal force acting on a boy is **20 N**.

### Problem #3

Calculate the centripetal force acting on a truck weighing 2500 kg, which moves with a velocity of 1.2 km/h in a circular path of radius 15 m.

**Solution**

Given data:

- Centripetal force acting on a truck, F
_{c}= ? - Mass of a truck, m = 2500 kg
- Velocity of a truck, v = 1.2 km/h = 0.33 m/s
- Radius of a circular path, r = 15 m

Applying the formula:

- F
_{c}= (m × v^{2}) ÷ r - F
_{c}= [2500 × (0.33)^{2}] ÷ 15 - F
_{c}= 272.25 ÷ 15 - F
_{c}= 18.15 N

Therefore, the centripetal force acting on a truck is **18.15 N**.

### Problem #4

Determine the centripetal force acting on a sports bike weighing 140 kg as it moves in a circular path with a radius of 25 m and a velocity of 2.5 km/h.

**Solution**

Given data:

- Centripetal force acting on a sports bike, F
_{c}= ? - Mass of a sports bike, m = 140 kg
- Radius of a circular path, r = 25 m
- Velocity of a sports bike, v = 2.5 km/h = 0.69 m/s

Applying the formula:

- F
_{c}= (m × v^{2}) ÷ r - F
_{c}= [140 × (0.69)^{2}] ÷ 25 - F
_{c}= 66.654 ÷ 25 - F
_{c}= 2.6 N

Therefore, the centripetal force acting on a sports bike is **2.6 N**.

## Related

- Force equation
- Normal force equation
- Net force formula
- Applied force formula
- Magnetic force equation
**Centripetal force equation**- Centrifugal force equation
- Spring force equation
- Tension force formula
- Electric force equation

## External links

- Centripetal Force Calculation – HyperPhysics Concepts
- 6.3 Centripetal Force – University Physics Volume 1 – OpenStax
- Centripetal Force Calculator – Omni Calculator
- Centripetal Force – Summary – The Physics Hypertextbook
- Centripetal Force – University of Notre Dame
- Centripetal force – Wikipedia
- Centripetal Force: Definition, Formula & Examples – Study.com
- 6.3: Centripetal Force – Physics LibreTexts
- 6.3 Centripetal Force – General Physics Using Calculus I – UCF Pressbooks
- Centripetal Force – CK-12
- The Centripetal Force Requirement – The Physics Classroom
- Centripetal Force and Velocity : Formula – Vaia
- AP Physics 1 : Centripetal Force and Acceleration – Varsity Tutors
- Centripetal and Centrifugal Acceleration Force – The Engineering ToolBox
- How to Find Centripetal Force – Sciencing
- What is a centripetal force? (article) – Khan Academy
- What Is Centripetal Force? Definition and Equations – ThoughtCo
- Centripetal Force: Definition, Examples, & Equation – Science Facts
- Centripetal Force Calculator – CalcTool
- How to Find Centripetal Force: Problem and Examples – Lambda Geeks
- Centripetal Force – Dummies
- Centripetal Force Formula – SoftSchools.com
- Centripetal Force Calculator – Calculator Academy

Deep

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