# Centrifugal force

Centrifugal force, also known as a fictitious force or pseudo force, is the apparent force that pushes an object outward when it is rotating around a center. Although it is not a real force, but rather a result of inertia, it appears to act on objects in a rotating reference frame. For instance, when you take a sharp turn in a car, you feel pushed outward against the car door. This sensation is due to your body’s inertia trying to keep you moving in a straight line while the car turns. In reality, it is the car exerting a centripetal force on you, pulling you inward. Centrifugal force is often observed in scenarios involving circular motion, such as amusement park rides and the spinning of a washing machine drum.

The equation for centrifugal force (Fcf) in a rotating reference frame is given by:

$$F_{cf} = \frac{mv^{2}}{r}$$

where m is the mass of the object, v is the velocity of the object, and r is the radius of the circular path. This equation is similar to that of centripetal force, showing that centrifugal force is the apparent force felt in a rotating system, acting outward from the center of rotation.

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## Practice problems

### Problem #1

Determine the centrifugal force acting on a scooter weighing 80 kg as it moves in a circular path with a radius of 16 m and a velocity of 2 m/s.

Solution

Given data:

• Centrifugal force acting on a scooter, Fc = ?
• Mass of a scooter, m = 80 kg
• Radius of a circular path, r = 16 m
• Velocity of a scooter, v = 2 m/s

Applying the formula:

• Fc = (m × v2) ÷ r
• Fc = [80 × (2)2] ÷ 16
• Fc = 320 ÷ 16
• Fc = 20 N

Therefore, the centrifugal force acting on a scooter is 20 N.

### Problem #2

Calculate the centrifugal force acting on a bike weighing 150 kg, which moves with a velocity of 1 km/h in a circular path of radius 5 m.

Solution

Given data:

• Centrifugal force acting on a bike, Fc = ?
• Mass of a bike, m = 150 kg
• Velocity of a bike, v = 1 km/h = 0.27 m/s
• Radius of a circular path, r = 5 m

Applying the formula:

• Fc = (m × v2) ÷ r
• Fc = [150 × (0.27)2] ÷ 5
• Fc = 10.935 ÷ 5
• Fc = 2.18 N

Therefore, the centrifugal force acting on a bike is 2.18 N.

### Problem #3

Find the centrifugal force acting on a girl weighing 24 kg who is enjoying a carousel ride. The girl sits on a carousel rotating in a circular path with a radius of 8 m and a velocity of 1 m/s.

Solution

Given data:

• Centrifugal force acting on a girl, Fc = ?
• Mass of a girl, m = 24 kg
• Radius of a circular path, r = 8 m
• Velocity of a girl, v = 1 m/s

Applying the formula:

• Fc = (m × v2) ÷ r
• Fc = [24 × (1)2] ÷ 8
• Fc = 24 ÷ 8
• Fc = 3 N

Therefore, the centrifugal force acting on a girl is 3 N.

### Problem #4

Determine the centrifugal force acting on a bus weighing 700 kg as it moves in a circular path with a velocity of 0.8 km/h. The radius of the circular path is 8 m.

Solution

Given data:

• Centrifugal force acting on a bus, Fc = ?
• Mass of a bus, m = 700 kg
• Velocity of a bus, v = 0.8 km/h = 0.22 m/s
• Radius of a circular path, r = 8 m

Applying the formula:

• Fc = (m × v2) ÷ r
• Fc = [700 × (0.22)2] ÷ 8
• Fc = 33.88 ÷ 8
• Fc = 4.23 N

Therefore, the centrifugal force acting on a bus is 4.23 N.