In physics, the centripetal force is used widely for circular motion. Centripetal force is a general type of force and is usually used for pulling the objects closer. This force keeps the object rotating in a circular path until it stopped manually.
In this post, we will learn about the definition and formulas of the centripetal force with a lot of examples.
What is centripetal force?
According to Wikipedia:
“A force that makes a body follow a circular path is known as the centripetal force. The direction of this force is always rectangular to the motion of the body towards the fixed point from the center of the curvature.”
In simple words, centripetal force is that force that keeps the object in the fixed path focused on the center of a curved path. The direction of the force is always parallel to the radius of the curvature from the center. The SI unit of centripetal force is newton (N) or kilograms meter per second square (kg m/s2).
The value of the centripetal force is based on three factors.
- The velocity of the object.
- The mass of the object.
- The distance from the center. Or radius of the curvature.
The equation of the centripetal force is written as:
F = m * v2 / r
In the above equation, F is the centripetal force of the object, r is the radius of the curvature, v is the velocity, and m is the mass of the object. By using this equation, we can also find the mass, velocity, and radius of the curvature if the centripetal force is given.
Mass = m = F * r / v2
Velocity = v = sqrt ((F * r)/ m)
Radius = r = m * v2 / F
You can use a centripetal force calculator to get the result of the questions according to the above formulas. Using this calculator, you have to select the term that you want to calculate. After that fill the required boxes and click the calculate button.
The result will show below the calculate button.
You can also see the steps by pressing show steps. The step-by-step solution will be shown below the answer.
How to calculate the problems of centripetal force?
You can easily calculate the centripetal force by using the formula. Let us take some examples to understand how to calculate the centripetal force.
Example 1: For centripetal force
Determine the centripetal force of an object if the mass of that object is 30 kg, the velocity of the object is 30 m/s, and the radius of curvature is 20 m.
Solution
Step 1: Write the given data values.
Mass = m = 30 kg
Velocity = v = 30 m/s
Radius of curvature = r = 20 m
Step 2: Now write the general equation to calculate the centripetal force.
F = m * v2 / r
Step 3: Now put the given values of mass, velocity, and radius in the above equation.
F = 30 kg * (30 m/s)2 / 20 m
F = (30 kg * 900 m2/s2) / 20 m
F = (27000 kgm2/s2) / 20 m
F = 1350 kg m/s2
F = 1350 N
Hence, the centripetal force of the given object is 1350 N.
Example 2: For the mass of the object
Determine the mass of the object whose centripetal force is 1398 N, the velocity of the object is 35 m/s, and the radius of curvature is 40 m.
Solution
Step 1: Write the given data values.
Centripetal force = F = 1398 N
Velocity = v = 35 m/s
Radius of curvature = r = 40 m
Step 2: Now write the general equation to calculate the mass of the object.
Mass = m = F * r / v2
Step 3: Now put the given values of the centripetal force, velocity, and radius in the above equation.
m = 1398 kg m/s2 * 40 m / (35 m/s )2
m = 1398 kg m/s2 * 40 m / 1225 m2/sec2
m = 55920 (kg m2/s2)/ 1225 (m2/sec2)
m = 55920 kg / 1225
m = 45.65 kg
Hence, the mass of the object is 45.65 kg.
Example 3: For the velocity of the object
Determine the velocity of the object whose centripetal force is 2797 N, the mass of the object is 155 kg, and the radius of curvature is 50 m.
Solution
Step 1: Write the given data values.
Centripetal force = F = 2797 N
Mass = m = 155 kg
Radius of curvature = r = 50 m
Step 2: Now write the general equation to calculate the velocity of the moving object.
Velocity = v = sqrt ((F * r)/ m)
Step 3: Now put the given values of the centripetal force, mass, and radius in the above equation.
v = sqrt ((2797 N* 50 m)/ 155 kg)
v = sqrt ((139850 kg m2/s2)/ 155 kg)
v = sqrt ((139850 m2/s2)/ 155)
v = sqrt (902.26 m2/s2)
v = 30.04 m/s
Hence, the velocity of the object is 30.04 m/s.
Example 4: For the radius of the curvature
Determine the radius of curvature of the moving object whose centripetal force is 3500 N, the mass of the object is 200 kg, and the velocity is 10 m.
Solution
Step 1: Write the given data values.
Centripetal force = F = 3500 N
Mass = m = 200 kg
Velocity = v = 10 m
Step 2: Now write the general equation to calculate the radius of the moving object.
Radius = r = m * v2 / F
Step 3: Now put the given values of the centripetal force, mass, and velocity in the above equation.
r = 200 kg * (10 m/s)2 / 3500 N
r = 200 kg * (100 m2/s2) / 3500 kg m/sec2
r = 20000 (kg m2/s2) / 3500 kg m/sec2
r = 20000 m / 3500
r = 5.71 m
Hence, the radius of the moving object is 5.71 m.
Summary
The centripetal force is not a difficult topic. Once you grab the basics of this topic, you can easily solve the numerical problems of the centripetal force. By using the formula of the centripetal force, you can easily calculate the centripetal force, mass, velocity, or radius of the curvature.