Motion in a Horizontal Plane
Figure shows a mass m tied to an end of a string of length L. The mass m moves in a horizontal plane with a constant speed. As the mass moves in the circle, the string sweeps a cone of an angle θ with the surface where θ is the angle made by the string with the normal. The forces that act on the mass m at any instant are shown in figure. If T is the tension in the string, then the components of T will be T cosθ and T sinθ. There is no vertical acceleration on m. So, the component T cos θ balances the weight W of m. This way
Fig:(b) Circular Motion in a horizontal plane
Here, the value of θ cannot be 90°, because then x will be zero or v = ∞.
The maximum value of τ will be
τmax = \(2 \pi \sqrt{\frac{L}{g}}\)
It is possible for very small angle (θ ≈ 0°) so that cosθ = cos 0° = 1.
Equation (5) represents the formula for the time period of a simple pendulum (we will study in chapter 8). With this similarty, the above device is called conical pendulum.
