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An insect trapped in a circular groove o...

An insect trapped in a circular groove of radius `12 cm` moves along the groove steadily and commpletes ` 7` revoltions in `100 s.` (a) What is the angulr speed , and thelinear speed of the motion ? (b) Is the acceleration vector a costant vector ? What is its magnitude?

Text Solution

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This is a case of uniform circular motion
Given, radius , r=12 cm
Frequency, `v=7//100 s^(-1)`
(a) Angular speed , `Omega=2piv=2xx(22)/(7)xx(7)/(100)=0.44 rad//s`
Linear speed , `v=romega=12xx0.44`
`=5.28 cm//s`
(b) Acceleration is always directed towards the centre of the groove . Since this direction changes continously as the velocity vector is along the tangent to the circle at every point , acceleration is not a constant vector . Magnitude of acceration is constant and is given by
`a=romega^(2)=12xx(0.44)^(2)=2.3 cm//s^(2)`
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