Question

Which graph best illustrates the relationship between the frequency of an object’s rotation as a function of the orbital radius? Note, centripetal force and mass are constant.

Answer 1

f = 2 * pi * r / v

So, 'f' increases linearly with 'r'

Therefore, picture 3. The straight line which increases along both axes.

Answer 2

@pompeii00 i think there's a little mistake in ur equation here actually,its
\[T=\frac{ 2 \pi R }{ V } \\where \\T=time~period~of ~revolution \\V=velocity~of ~the ~object \\T=radius\]
again we know that--
\[T=\frac{ 1 }{ frequency }=\frac{ 1 }{ F } \\ so \\F=\frac{ 1 }{ T }=\frac{ 1 }{ \frac{ 2 \pi R }{ V } }=\frac{ V }{ 2 \pi R }\]
so whAT we can see here is that frequency is inversely proportional to the radius of the orbit
\[F ~~~\alpha~~~\frac{ 1 }{ R }\]
so the graph should be a rectangular hyperbola like in option (A)

Answer 3

got this? @lolo123...