# 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 with velocity experiences an acceleration directed toward the center of its path,

.

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 :

and then equating this to the centripetal acceleration,

We can show that the centripetal force has magnitude

and is always directed towards the center of the circular path. Equivalently, if is the angular velocity then because ,

# Tethered ball

One apparatus that clearly illustrates the centripetal force consists of a tethered mass () swung in a horizontal circle by a lightweight string which passes through a vertical tube to a counterweight () as shown in Figure 1.

**Exercise 1:**If is a $1~\mathrm{kg}$ mass spinning in a circle of radius $1~\mathrm{m}$ and $m_2 = 4~\mathrm{kg}$ what is the angular velocity assuming neither mass is moving vertically and there is minimal friction between the string and tube?

# Wind turbine

**Exercise 2a:**A large wind turbine has blades of 35 m in length, each weighing 10,000 kg. The center of mass of a blade is located halfway along its length. If the turbine is rotating at 20 revolutions per minute, what tension force are the bolts under as they hold a spinning blade to the hub?