A particle is rotating about a vertical axis in the horizontal plane such that the angular velocity of the particle about the axis is constant and is equal to 1 rad/s. Distance of the particle from axis is given by R=R0-β t where t stands for time. The speed of the particle as a function of time is

Question

A particle is rotating about a vertical axis in the horizontal plane such that the angular velocity of the particle about the axis is constant and is equal to 1 rad/s. Distance of the particle from axis is given by R=R0-β t where t stands for time. The speed of the particle as a function of time is (A) √β 2 + 1 (B) (R0 - β t) (C) √β 2 + R0 - β t2 (D) β

Tardigrade Admin · Accepted Answer

V textradial=(d R/d t)=-β V texttangential=ω R=ω R0 - β t V=√Vr2 + Vt2=√β 2 + R0 - β t2

$β^{2} + 1$

$(R_{0} - βt)$

$β^{2} + R_{0} - β t^{2}$

$β$

$V_{radial} = \frac{d R}{d t} = - β$
$V_{tangential} = ω R = ω R_{0} - βt$
$V = V_{r}^{2} + V_{t}^{2} = β^{2} + R_{0} - β t^{2}$

β2+1​

(R0​−βt)

β2+R0​−βt2​

β

Vradial​=dtdR​=−β Vtangential​=ωR=ωR0​−βt V=Vr2​+Vt2​​=β2+R0​−βt2​

$β^{2} + 1$

$(R_{0} - βt)$

$β^{2} + R_{0} - β t^{2}$

$β$

$V_{radial} = \frac{d R}{d t} = - β$
$V_{tangential} = ω R = ω R_{0} - βt$
$V = V_{r}^{2} + V_{t}^{2} = β^{2} + R_{0} - β t^{2}$