Equation of arc and rotation

Illustration on Rotation Theorem|| Complex Equation OF Circle and Straight line

The fastest possible rate of rotation of a planet is that for which the gravitational force on material at the equator just nearly provides the centripetal force needed for rotation. The corresponding shortest period of rotation is (If rho is the density of the earth)

If ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is rotated 90^(@) about origin,the equation of ellipse after rotation is

Equation and Fixed Axis Rotation

Equation OF Rotating Liquid|| Force on Side Walls by Liquid

If ABC is an arc of a circle and /_ABC=135^(@), then the ratio of arc ABC to the circumference is :

The graph that represents variation of g at the equator with square of angular velocity of rotation of earth is

If the speed of rotation of earth about its axis increases, then the weight of the body at the equator will

Length of an Arc

Length of an arc