In non-uniform circular motion, the ratio of tangential to radial acceleration is ( r= radius of the circle, u= speed of the particle, α = angular acceleration)

Question

In non-uniform circular motion, the ratio of tangential to radial acceleration is ( r= radius of the circle, u= speed of the particle, α = angular acceleration) (A) (α 2 r2/u) (B) (α 2 r /u2) (C) (α r2/u2) (D) (u2/r2 α )

Tardigrade Admin · Accepted Answer

Tangential acceleration = α r Radial acceleration = (u2/r) Ratio = (α r/u2 / r) = (α r2/u2)

Q. In non-uniform circular motion, the ratio of tangential to radial acceleration is ( $r =$ radius of the circle, $u =$ speed of the particle, $α =$ angular acceleration)

$\frac{α ^{2} r ^{2}}{u}$

$\frac{α ^{2} r}{u ^{2}}$

$\frac{α r ^{2}}{u ^{2}}$

$\frac{u ^{2}}{r ^{2} α}$

Tangential acceleration $= α r$
Radial acceleration $= \frac{u ^{2}}{r}$
Ratio $= \frac{α r}{u ^{2} / r} = \frac{α r ^{2}}{u ^{2}}$

Q. In non-uniform circular motion, the ratio of tangential to radial acceleration is ( r= radius of the circle, u= speed of the particle, α= angular acceleration)

uα2r2​

u2α2r​

u2αr2​

r2αu2​