Question

Can someone please help me with this

Answer 1

hmmm proofs like these can be a bit circular kinda, let's do some rigamarole on the equations and we'll see if that works for a definition

`\stackrel{\theta \textit{ is always in radian unit}~\hfill }{s=r\theta\implies \cfrac{s}{\theta }=r \hspace{5em}v=\cfrac{s}{t}\implies t=\cfrac{s}{v}\hspace{5em}\omega=(\theta )/(t)} \\\\[-0.35em] ~\dotfill\\\\ \omega=\cfrac{\theta }{t}\implies \omega=\cfrac{\theta }{~~ ( s)/(v ) ~~}\implies \omega=\cfrac{\theta }{1}\cdot \cfrac{v}{s}\implies \omega=\cfrac{\theta v}{s}\implies s\omega=\theta v \\\\\\ \cfrac{s\omega}{\theta }=v\implies \cfrac{s}{\theta }\cdot \omega=v\implies \boxed{r\cdot \omega=v}`