Question

A stone tied to the end of 20 cm long string is whirled in a horizontal circle. If the centripetal acceleration is 9.8 ms-2, its angular speed in radian per sec is :

Answer 1

Answer on Question #60208, Physics / Mechanics | Relativity

A stone tied to the end of 20 cm long string is whirled in a horizontal circle. If the centripetal acceleration is 9.8 ms-2, its angular speed in radian per sec is :

Find: $\omega - ?$

Given:

$$\begin{array}{l} r = 0,2 \, \text{m} \\ a_c = 9,8 \, \text{m/s}^2 \end{array}$$

Solution:

The relationship between linear velocity $v$ and cyclic velocity $\omega$:

$$v = \omega r \, (1),$$

where $r$ – radius of the circle

$$\text{Of} \, (1) \Rightarrow \omega = \frac{v}{r} \, (2)$$

Centripetal acceleration:

$$a_c = \frac{v^2}{r} \, (3)$$ $$\text{Of} \, (3) \Rightarrow v = \sqrt{a_c r} \, (4)$$ $$(4) \text{ in } (2): \omega = \sqrt{\frac{a_c}{r}} \, (5)$$ $$\text{Of} \, (5) \Rightarrow \omega = 7 \, \text{rad/s}$$

Answer:

7 rad/s

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