Question

Example 4.10 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 1

Question :-

$⟶$An insect trapped in circular groove of radius 12 cm moves along the groove steadily and completes revolutions in 100 s. (a) What is the angular speed of motion? (b) Is the acceleration vector constant ? What is its magnitude?

➮ Given :-

$⟶$r = 12cm = 0.12m

$⟶$Time to complete one revolution, t = 100 s

➮ To find :-

$⟶$What is the angular speed of motion?

$⟶$What is its magnitude?

➮ Formula required :-

$\boxed{\sf Average \: speed = 2πr/T}$

$\green{\bold{\boxed{Angular \: speed = w/r}}}$

➮ Solution :-

$average speed = \frac{2πr}{T}$

$⟹\frac{2π × 0.12}{100}$

$⟹0.0075m/s \: = \: 0.75cm/s$$angular speed \: w = \frac{v}{r}$

$⟹\frac{0.0075}{0.12} = 0.0625rad/s$

Centripetal acceleration changes its direction at every instant.

Magnitude of acceleration $a = \frac{v²}{r}$

$⟹4.7 \times {10}^{-4} m/s²$

$⟹ <strong>0.047 cm/s²</strong>$