The angular speed in terms of m, R, and g is √2g/R
To find the angular speed when the small object is directly below the axis, use the conservation of energy.
The initial potential energy is converted into kinetic energy.
The gravitational potential energy at the beginning is mgh.
Where;
m is the mass
g is the acceleration due to gravity
h is the height.
The kinetic energy at the bottom (when the object is directly below the axis) is given by (1/2)mv².
where; v is the linear speed.
Setting these equal and solving for v, relate linear speed (v) to angular speed (ω) using the formula v = Rω
where; R is the radius.
The resulting expression for angular speed in terms of m, R, and g is:
ω = √2g/R
This assumes no energy losses due to friction or air resistance.
Therefore, the angular speed in terms of m, R, and g is √2g/R