A flywheel of mass 50 kg and radius of gyration about its axis of rotation of 0.5 m is acted u

step 1 In this question we have given a flywheel of mass 50 kilograms and radius of gyration about its

A flywheel of mass 50 kg and radius of gyration about its...

A flywheel of mass $50 \mathrm{~kg}$ and radius of gyration about its axis of rotation of $0.5 \mathrm{~m}$ is acted upon by a constant torque of $12.5 \mathrm{~N}-\mathrm{m}$. Its angular velocity at $t=5$ seconds is (a) $2.5 \mathrm{rad} / \mathrm{s}$ (b) $5 \mathrm{rad} / \mathrm{s}$ (c) $7.5 \mathrm{rad} / \mathrm{s}$ (d) $10 \mathrm{rad} / \mathrm{s}$

A flywheel of mass $50 \mathrm{~kg}$ and radius of gyration about its axis of rotation of $0.5 \mathrm{~m}$ is acted upon by a constant torque of $12.5 \mathrm{~N}-\mathrm{m}$. Its angular velocity at $t=5$ seconds is
(a) $2.5 \mathrm{rad} / \mathrm{s}$
(b) $5 \mathrm{rad} / \mathrm{s}$
(c) $7.5 \mathrm{rad} / \mathrm{s}$
(d) $10 \mathrm{rad} / \mathrm{s}$

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Key Concepts

Angular Kinematics

Angular kinematics involves the equations that describe the angular displacement, angular velocity, and angular acceleration of a rotating object, analogous to linear kinematics. When the angular acceleration is constant, these equations allow one to compute the angular velocity after a given time, starting from an initial state.

Newton's Second Law for Rotational Motion

Newton's Second Law for Rotation states that the net torque acting on a body is equal to the product of its moment of inertia and its angular acceleration (? = I?). This principle is crucial for determining the angular acceleration when a known torque is applied, forming the basis for solving rotational dynamics problems.

Moment of Inertia

The moment of inertia is a measure of an object's resistance to change in its rotational motion. It depends on the mass distribution of the object with respect to the axis of rotation, and in problems like this, it is often calculated using the radius of gyration to simplify the relationship.

Radius of Gyration

The radius of gyration represents the distance from the axis of rotation at which the mass of the body can be thought to be concentrated to produce the same moment of inertia. It is a useful concept for calculating the moment of inertia when the mass distribution is known through this single parameter.

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