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A wheel of radius 0.2 m rotates freely about its center when a string that is wrapped over its rim is pulled by force of 10 N as shown in the figure below. The established torque produces an angular acceleration of 2 rad/s$$^2$$. Moment of inertia of the wheel is _________ kg m$$^2$$.
(Acceleration due to gravity = 10 m/s$$^2$$)
Correct Answer: 1
The torque produced by the force acting tangentially at the rim is:
$$\tau = F \cdot R$$
$$\tau = 10 \text{ N} \times 0.2 \text{ m} = 2 \text{ N m}$$
$$I = \frac{\tau}{\alpha}$$
$$I = \frac{2}{2}$$
$$I = 1 \text{ kg m}^2$$
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