If the body describes a vertical circle then the minimum velocity at an
angle 'O' from lowest position is
To determine the minimum velocity of a body at an angle 'θ' from the lowest position in vertical circular motion, you can use the concept of conservation of mechanical energy.
In vertical circular motion, the body experiences both gravitational potential energy and kinetic energy. At the lowest point of the circle, all the mechanical energy is in the form of kinetic energy, and at the highest point, all the mechanical energy is in the form of gravitational potential energy.
The minimum velocity occurs at the highest point of the circle, where the body momentarily comes to rest before reversing its direction. At this point, the kinetic energy is zero and the entire mechanical energy is in the form of gravitational potential energy.
To find the minimum velocity, we equate the gravitational potential energy at the highest point to the initial mechanical energy at the lowest point:
mgh = 1/2 mv^2
Where:
m = mass of the body
g = acceleration due to gravity
h = height of the highest point (which equals the radius of the circle)
Now, we can solve for the minimum velocity, v:
v = √(2gh sin²θ)
Where:
θ = angle from the lowest position
By plugging in the values of mass, acceleration due to gravity, height, and angle, you can calculate the minimum velocity of the body at an angle 'θ' from the lowest position in a vertical circle.