Centripetal Force: Definition, Formula/Equation and Examples

What is Centripetal Force?

Have you ever thought why the moon and other satellites move in round orbit around the earth? This is due to force- the Centripetal force.

Any motion in a curved path shows accelerated movement and demands that the force be directed toward the middle of the curvature of the path. This force is called the centripetal force which means “enter seeking” force (Latin centrum, “center” and petere, “to seek”).

Table of Contents Hide

1) Definition of Centripetal force
2) Explanation:
3) Mathematical form:
4) Centripetal force requirement
5) MCQs about Centripetal Force
6) Conclusion
- 6.1) Examples and Significance
7) You may also like to learn:

Definition of Centripetal force

Centripetal force is a force which maintains an object to move into a circle.

Explanation:

Consider a body attached at the ending of a string moving with uniform speed in a curved path. A body tends to move in a straight line due to inertia. The string to which the body is attached retains it to move in a circle by pulling the body to the center of the circle. The string brings the entire body perpendicular to the motion.

This pulling force continuously changes the direction of motion and stays towards the center of the circle. This center seeking force is called the centripetal force. It keeps your system to move into a circle. Centripetal force always acts perpendicular to the motion of the object.

Mathematical form:

Let a body of mass m moves with uniform speed v at a circle of radius r. The acceleration a produced by the c

centripetal force F is given by

centripetal acceleration $\fn_jvn \large a_c=v^2/r$

According to 2^nd law of newton

F=ma

For centripetal force

F_{c =}m a_c

Now by putting the value of a_cin 2^nd law equation: $\fn_jvn \large F_c=(mv^2)/r{\color{Purple} }$

The centripetal force needed by a body moving in a circle is dependent upon the mass of body m, square of its velocity v, and reciprocal to the radius r of the circle.

Now study the centripetal force in the following examples

a stone attached to an end of a string rotating in a circle. The tension T in the string supplies the required centripetal force. It keeps the stone to stay in the circle. If the string is not strong enough to supply the essential tension, then it breaks and the stone moves off along a tangent to the circle.

The moon revolves around the Earth. The gravitational force of the planet earth supplies the necessary centripetal force.

Centripetal force requirement

A body moving at a circle is experiencing an acceleration. Even moving in the circular path with constant speed, the velocity still changes and hence the change in acceleration. This change in velocity is directed towards the center of this circle. And according to Newton’s 2nd law of motion, a thing that experiences an acceleration should be undergoing a net force.

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The direction of the net force is precisely the exact same way as the acceleration. Therefore, for an object moving at a circle, there has to be an inward force acting upon it as a way to maintain its inward acceleration. That is occasionally known as the centripetal force condition. The term centripetal (never to be mistaken with the fword centrifugal) means centre seeking. For things moving in a circular motion, there’s a net force acting towards the centre that results in the object to seek center of circle.

Based on Newton’s first law of motion; the law of inertia, it is the natural tendency of most moving objects to keep motion in precisely the exact same way they are moving… unless any sort of unbalanced force acts upon the object to change its motion from its straight-line path. So, the objects moving in a straight path require some unbalanced force to turn them in a circular motion and that is the requirement of centripetal force.

MCQs about Centripetal Force

MCQ 1: What is the definition of centripetal force?
- A) A force that pushes objects away from the center
- B) A force that maintains an object’s motion in a straight line
- C) A force that maintains an object’s motion in a circle
- D) A force that increases an object’s velocity
Answer: C) A force that maintains an object’s motion in a circle
MCQ 2: What does the term “centripetal” mean?
- A) Moving outward from the center
- B) Moving inward toward the center
- C) Moving parallel to the center
- D) Moving perpendicular to the center
Answer: B) Moving inward toward the center
MCQ 3: Which force continuously changes the direction of motion and stays towards the center of the circle?
- A) Centrifugal force
- B) Frictional force
- C) Centripetal force
- D) Gravitational force
Answer: C) Centripetal force
MCQ 4: According to Newton’s second law, what is the mathematical expression for centripetal force?
- A) F = m/v
- B) F = m/a
- C) F = ma
- D) F = mv^2/r
Answer: D) F = mv^2/r
MCQ 5: In the example of a stone attached to a string rotating in a circle, what supplies the necessary centripetal force?
- A) Gravitational force
- B) Tension in the string
- C) Frictional force
- D) Inertia of the stone
Answer: B) Tension in the string
MCQ 6: What force supplies the necessary centripetal force for the moon to revolve around the Earth?
- A) Solar radiation
- B) Gravitational force of the moon
- C) Gravitational force of the Earth
- D) Tidal force
Answer: C) Gravitational force of the Earth
MCQ 7: What does Newton’s second law of motion state regarding objects experiencing acceleration?
- A) They do not experience any force
- B) They experience a net force
- C) They move at a constant speed
- D) Their velocity remains unchanged
Answer: B) They experience a net force
MCQ 8: According to Newton’s first law of motion, what is the natural tendency of moving objects?
- A) To accelerate
- B) To move in a straight line
- C) To change direction randomly
- D) To slow down
Answer: B) To move in a straight line
MCQ 9: What is the requirement for an object to move in a circular path according to Newton’s first law of motion?
- A) Balanced force
- B) Centrifugal force
- C) Unbalanced force
- D) Gravitational force
Answer: C) Unbalanced force
MCQ 10: What does the term “centripetal force condition” refer to?
- A) Outward force acting on an object
- B) Inward force maintaining circular motion
- C) Force parallel to the circle’s radius
- D) Force acting perpendicular to the motion
Answer: B) Inward force maintaining circular motion
MCQ 11: Which law of motion describes the tendency of objects to maintain their state of motion?
- A) Newton’s first law
- B) Newton’s second law
- C) Newton’s third law
- D) Law of universal gravitation
Answer: A) Newton’s first law
MCQ 12: What is the direction of the net force for an object moving in a circular path?
- A) Away from the center
- B) Tangential to the path
- C) Toward the center
- D) Opposite to the direction of motion
Answer: C) Toward the center
MCQ 13: What happens to the velocity of an object moving in a circular path?
- A) It decreases
- B) It remains constant
- C) It increases
- D) It changes direction
Answer: D) It changes direction
MCQ 14: What is the relationship between the centripetal force and the mass of the object?
- A) Directly proportional
- B) Inversely proportional
- C) No relationship
- D) Linear relationship
Answer: A) Directly proportional
MCQ 15: What is the relationship between the centripetal force and the square of the velocity of the object?
- A) Directly proportional
- B) Inversely proportional
- C) No relationship
- D) Exponential relationship
Answer: A) Directly proportional
MCQ 16: What is the relationship between the centripetal force and the radius of the circle?
- A) Directly proportional
- B) Inversely proportional
- C) No relationship
- D) Exponential relationship
Answer: B) Inversely proportional
MCQ 17: What is the unit of centripetal acceleration?
- A) m/s^2
- B) m/s
- C) m^2/s
- D) s/m^2
Answer: A) m/s^2
MCQ 18: What does the centripetal force act perpendicular to?
- A) The object’s velocity
- B) The object’s acceleration
- C) The object’s direction of motion
- D) The object’s radius
Answer: D) The object’s radius
MCQ 19: What is the term used for the force that pushes objects outward from the center of rotation?
- A) Centripetal force
- B) Gravitational force
- C) Centrifugal force
- D) Tension force
Answer: C) Centrifugal force

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Conclusion

In conclusion, centripetal force plays a crucial role in maintaining the circular motion of objects, whether it’s the moon orbiting the Earth or a stone swinging on a string.

Definition and Importance

Centripetal force is defined as the force directed towards the center of curvature. It ensures that objects continue along their curved paths rather than moving in a straight line due to inertia.

Mechanism and Application

This force, often supplied by tension or gravitational attraction, keeps objects moving in a circular trajectory by continuously changing their direction of motion. Understanding the principles of centripetal force, as governed by Newton’s laws of motion, sheds light on the mechanics behind circular motion and the requirement for inward forces to sustain it.

Examples and Significance

Through examples and mathematical formulations, the tutorial elucidates the significance of centripetal force in various scenarios, emphasizing its role in maintaining acceleration and keeping objects on their circular paths.