(a) A body of mass m kg is attached to a point by string of length
1.25 m. If the mass is rotating in a horizontal circle 0.75 m below the
point of attachment, calculate its angular velocity.

(b) If the mass rotates on a table, calculate the force on the table when
the speed of rotation is 25 rpm and the mass is 6 kg.

 

a) first the geometry: we have a rectangular triangle formed by the radius of rotation, the distance between the attach point of the string and the plane of rotation and the string. Solving that gives a radius of rotation of 1 m.
Then the mechanic: the centripetal acceleration on the mass is radius * angular velocity squared. This is pulling horizontally and gravity is pulling down. The ratio of these two is in line with the string and is 1 m / 0.75 m = (radius * angular velocity squared) / g