Question

..
An insect trapped in a circular groove of radius 12 cm moves along the groove
steadily and completes 10 revolutions in 100 s. (a) What is the angular speed and
liner speed of the motion (b) Is the acceleration vector a constant vector? What
is its magnitude?
​

Answer 1

$(a) : 0.024\pi \: m {s}^{ - 1} \\ \: \: \: \: (b) : 0.0048 {\pi}^{2} \: m {s}^{ - 2}$

Explanation:

$Given, \: \: r = 12 \: cm = 0.12 \: m \: \: \: and \: \: \: n = \frac{10}{100} {s}^{ - 1} = 0.1 {s}^{ - 1} \\(a) : \: we \: \: know \: \: \boxed{ \omega = 2\pi n \: \: \: and \: \: \: v = \omega \times r} \\ Now, \: \: \: v = \omega \times r = 2\pi n \times r \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times \pi \times 0.1 {s}^{ - 1} \times 0.12 \: m \\ \: \: \: \: \: \: \: \: \: = \boxed{ 0.024\pi \: m {s}^{ - 1} } \\ (b) : \: we \: \: know \: \: \boxed{a = \frac{ {v}^{2} }{r} } \\ a = \frac{(0.024\pi \: m {s}^{ - 1})^{2} }{0.12 \: m} \\ \: \: = \frac{0.000576 {\pi}^{2} }{0.12} \: m {s}^{ - 2} \\ = \boxed{ 0.0048 {\pi}^{2} \: m {s}^{ - 2} }$