Question

the normal acceleration of a point on the rim of a 3 m diameter fly wheel is a constant 15 m/s2 . The angular speed of the fly wheel is (in radian/s)
a)3.6
b)4.6
c)2.6
d)5.6​

Answer 1

Answer:

4.6

is the right answer

Answer 2

Given:

The normal acceleration of a point on the rim of a 3 m diameter fly wheel is a constant 15 m/s².

To find:

Angular speed of fly wheel ?

Calculation:

$\therefore \: a_{centripetal} = 15 \: m {s}^{ - 2}$

$\implies \: \dfrac{ {v}^{2} }{r} = 15$

$\implies \: \dfrac{ {v}^{2} }{( \frac{3}{2}) } = 15$

$\implies \: {v}^{2} = 15 \times 1.5$

$\implies \: {v}^{2} =22.5$

$\implies \: v = 4.74 \: m {s}^{ - 1}$

Now, let angular velocity be $\omega$:

$\therefore \: \omega = \dfrac{v}{r}$

$\implies \: \omega = \dfrac{4.74}{( \frac{3}{2}) }$

$\implies \: \omega = \dfrac{4.74}{1.5 }$

$\implies \: \omega = 3.16 \: rad \: {s}^{ - 1}$

So, angular speed is 3.16 rad/s.