An insect trapped in a circular groove of radius $12 \;cm$ moves along the groove steadily and completes $7$ revolutions in $100\; s$.
$(a)$ What is the angular speed, and the linear speed of the motion?
$(b)$ Is the acceleration vector a constant vector ? What is its magnitude ?
An insect trapped in a circular groove of radius $12 \;cm$ moves along the groove steadily and completes $7$ revolutions in $100\; s$.
$(a)$ What is the angular speed, and the linear speed of the motion?
$(b)$ Is the acceleration vector a constant vector ? What is its magnitude ?
Answer This is an example of uniform circular motion. Here $R=12 cm .$ The angular speed $\omega$ is given by
$\omega=2 \pi / T=2 \pi \times 7 / 100=0.44 rad / s$
The linear speed $v$ is :
$v=\omega R=0.44 s ^{-1} \times 12 cm =5.3 cm s ^{-1}$
The direction of velocity $v$ is along the tangent to the circle at every point. The acceleration is directed towards the centre of the circle. since this direction changes continuously. acceleration here is not a constant vector. However, the magnitude of acceleration is constant:
$a=\omega^{2} R=\left(0.44 s ^{-1}\right)^{2}(12 cm )$
$=2.3 cm s ^{-2}$
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- [AIEEE 2012]