What is the tension in a string in circular motion?

The tension in a string in circular motion is equal to the centripetal force.

When an object moves in a circular path, it experiences a force towards the center of the circle, known as the centripetal force. This force is provided by the tension in the string, if the object is attached to the string and is moving in a horizontal circle. Therefore, the tension in the string is equal to the centripetal force.

The centripetal force can be calculated using the formula F = mv²/r, where F is the centripetal force, m is the mass of the object, v is its velocity, and r is the radius of the circle. If the object is attached to a string, the tension in the string must be equal to the centripetal force, so we can write:

T = mv²/r

where T is the tension in the string.

For example, consider a ball of mass 0.2 kg attached to a string of length 0.5 m, moving in a horizontal circle with a velocity of 2 m/s. The radius of the circle is given by the length of the string, so r = 0.5 m. The centripetal force is:

F = mv²/r = 0.2 x 2²/0.5 = 1.6 N

Therefore, the tension in the string is also 1.6 N.

To understand how these principles apply in various scenarios, explore real-world applications of circular motion. For a deeper dive into the mathematical constants used in these equations, refer to types of numbers. Additionally, learning about applications of differentiation can further enhance your understanding of how velocity affects the tension in different contexts.

A-Level Maths Tutor Summary: In circular motion, the tension in a string equals the centripetal force, calculated using the formula 𝑇 = 𝑚𝑣^2/𝑟​. This formula means that the force keeping an object moving in a circle (centripetal force) is provided by the string's tension. For example, a 0.2 kg ball moving at 2 m/s on a 0.5 m string has a tension of 1.6 N.