Question

A torque of 10Nm is applied to a fly wheel of mass 10kg. And radius of gyration 50cm. What is the resulting angular acceleration?

Answer 1

The resulting angular acceleration is $4\ rad/s^2$.

Explanation:

Given that,

Torque applied to a fly wheel, $\tau=10\ N-m$

Mass of the wheel, m = 10 kg

Radius of gyration, r = 50 cm = 0.5 m

We need to find the resulting angular acceleration. The relation between torque and angular acceleration is given by :

$\tau=I\alpha$

I is the moment of inertia

The radius of gyration is given by :

$R=\sqrt{\dfrac{I}{m}} \\\\I=R^2m\\\\I=(0.5)^2\times 10\\\\I=2.5\ kg-m^2$

So,

$\alpha =\dfrac{\tau}{I}\\\\\alpha =\dfrac{10}{2.5}\\\\\alpha =4\ rad/s^2$

So, the resulting angular acceleration is $4\ rad/s^2$. Hence, this is the required solution.

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Moment of inertia

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