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## Main Question or Discussion Point

If a ball rolls in a semicircular track starting from one end of track,( the track is kept vertical) and if radius of ball is r and radius of track is R

is this expression correct? (When ball reaches lowest point)

##mg(R-r)=\frac{1}{2}I_0\omega^2 + \frac{1} {2}I\omega_1^2+\frac{1}{2}mv^2##

where ##I_0## is the moment of inertia about centre of track since the ball moves in a circle and moment of inertia is mr^2

The second is for rotation of ball

the third is translational kinetic energy

is this expression correct? (When ball reaches lowest point)

##mg(R-r)=\frac{1}{2}I_0\omega^2 + \frac{1} {2}I\omega_1^2+\frac{1}{2}mv^2##

where ##I_0## is the moment of inertia about centre of track since the ball moves in a circle and moment of inertia is mr^2

The second is for rotation of ball

the third is translational kinetic energy

**what changes should I make if R is very very larger than r?**