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## Physics library

### Course: Physics library>Unit 4

Lesson 2: Centripetal forces

# What is a centripetal force?

Learn what centripetal forces are and how to calculate them.

# What is a centripetal force?

A centripetal force is a net force that acts on an object to keep it moving along a circular path.
In our article on centripetal acceleration, we learned that any object traveling along a circular path of radius r with velocity v experiences an acceleration directed toward the center of its path,
a, equals, start fraction, v, squared, divided by, r, end fraction.
However, we should discuss how the object came to be moving along the circular path in the first place. Newton’s 1ˢᵗ law tells us that an object will continue moving along a straight path unless acted on by an external force. The external force here is the centripetal force.
It is important to understand that the centripetal force is not a fundamental force, but just a label given to the net force which causes an object to move in a circular path. The tension force in the string of a swinging tethered ball and the gravitational force keeping a satellite in orbit are both examples of centripetal forces. Multiple individual forces can even be involved as long as they add up (by vector addition) to give a net force towards the center of the circular path.
Starting with Newton's 2ⁿᵈ law :
a, equals, start fraction, F, divided by, m, end fraction
and then equating this to the centripetal acceleration,
start fraction, v, squared, divided by, r, end fraction, equals, start fraction, F, divided by, m, end fraction
We can show that the centripetal force F, start subscript, c, end subscript has magnitude
F, start subscript, c, end subscript, equals, start fraction, m, v, squared, divided by, r, end fraction
and is always directed towards the center of the circular path. Equivalently, if omega is the angular velocity then because v, equals, r, omega,
F, start subscript, c, end subscript, equals, m, r, omega, squared

# Tethered ball

One apparatus that clearly illustrates the centripetal force consists of a tethered mass (m, start subscript, 1, end subscript) swung in a horizontal circle by a lightweight string which passes through a vertical tube to a counterweight (m, start subscript, 2, end subscript) as shown in Figure 1.
Figure 1: Demonstration of a centripetal force provided by a mass m2 holding a spinning tethered ball.
Figure 1: _Demonstration of a centripetal force provided by a mass m, start subscript, 2, end subscript holding a spinning tethered ball._
Exercise 1: If m, start subscript, 1, end subscript is a 1, space, k, g mass spinning in a circle of radius 1, space, m and m, start subscript, 2, end subscript, equals, 4, space, k, g what is the angular velocity assuming neither mass is moving vertically and there is minimal friction between the string and tube?

# Car turns a corner

Exercise 2: A car turns a corner on a level street at a speed of 10, start text, space, m, slash, s, end text while sweeping out a circular path of radius 15, start text, space, m, end text. What is the minimum coefficient of static friction between the tires and the ground for this car to make the turn without slipping?