Question

A particle A moves along a circle of radius $R=10cm$ so that its radius vector $\overrightarrow{r}$ relative to O rotates with constant angular velocity $\omega =0.2rad/s$. Find the magnitude of the velocity of the particle and its total acceleration.

• A. $4cm/s,1.6cm/s^2$
• B. $4cm/s,2.6cm/s^2$
• C. $12cm/s,1.6cm/s^2$
• D. $12cm/s,1.8cm/s^2$

Answer 1

The correct option is A $4cm/s,1.6cm/s^2$


Given that ${\omega }_0=0.2rad/s,R=10cm=0.1m$
${\theta }_c=2{\theta }_o$ (from property of circle)
$\Rightarrow$ ${\omega }_c=2{\omega }_o=0.4rad/s$
(i) Magnitude of velocity $|\overrightarrow{v}|={\omega }_c\times R=\left(0.4\right)\left(0.1\right)$
$\Rightarrow |\overrightarrow{v}|=0.04m/s$ or $4cm/s$
(ii) Magnitude of total acceleration $|\overrightarrow{a}|={\omega }_c^2\times R$ (for uniform circular motion)
$\Rightarrow |\overrightarrow{a}|=\left(0.4{)}^2\right(0.1)=0.016m/s^2$
$\Rightarrow |\overrightarrow{a}|=1.6cm/s^2$