a circular wheel can rotate about its central axis which is vertical from a point on the rim hangs - Science - Wave Motion

Question

a circular wheel can rotate about its central axis which is
vertical from a point on the rim hangs a simple pendulum When the
wheel is caused to rotate uniformly, the angle of inclination of
the pendulum to the vertical is theta nod If the radius of the
wheel is R and length of pendulum is L, the rotatory frequency of
the wheel is​

Abhishek Singh · Accepted Answer

Dear Student,

This simple pendulum will act as a conical pendulum as the wheel rotates
The bob of the pendulum will perform circular motion
r=R+Lsinθ = radius of rotaion of bob
m- mass of bob (consideration)
mg - downwar force on bob due to mass
T- tension in string
w-angular speed of wheel
T can be resolved in horizontal and vertical component as in diagram
angular speed of wheel is same as the speed of bob
Tcosθ=mg Tsinθ=mrw2divde above equation we get,TcosθTsinθ=mgmrw2cotθ=grw2cotθ=g(R+Lsinθ)
w2w =gtanθ(R+Lsinθ)
Regards