A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. If t

step 1 In this question we have given a rope of negligible mass and it is wound around a hollow cylinde

A rope of negligible mass is wound round a hollow cylinder...

A rope of negligible mass is wound round a hollow cylinder of mass $3 \mathrm{~kg}$ and radius $40 \mathrm{~cm}$. If the rope with a force of $30 \mathrm{~N}$, then the angulat is pulled acceleration produced in the cylinder is (b) $20 \mathrm{rad} \mathrm{s}^{-2}$ (a) $15 \mathrm{rad} s$ (d) $30 \mathrm{rad} \mathrm{s}^{-2}$ (c) 25 rad $s^{-2}$, her 62 , the linear acceleration

A rope of negligible mass is wound round a hollow cylinder of mass $3 \mathrm{~kg}$ and radius $40 \mathrm{~cm}$. If the rope with a force of $30 \mathrm{~N}$, then the angulat is pulled acceleration produced in the cylinder is
(b) $20 \mathrm{rad} \mathrm{s}^{-2}$
(a) $15 \mathrm{rad} s$
(d) $30 \mathrm{rad} \mathrm{s}^{-2}$
(c) 25 rad $s^{-2}$, her 62 , the linear acceleration

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Key Concepts

Torque

Torque is the measure of a force’s ability to produce rotation about an axis. It is calculated as the product of the force and the perpendicular distance (lever arm) from the axis of rotation. In problems like this, torque is used to determine the rotational effect produced by a force acting on a body.

Moment of Inertia

The moment of inertia quantifies an object's resistance to changes in its rotational motion. It depends on both the mass of the object and the distribution of that mass relative to the axis of rotation. For a hollow cylinder, this is specifically calculated as I = m·r², which is crucial for solving rotational dynamics problems.

Newton's Second Law for Rotation

Newton's second law for rotational motion states that the net torque acting on an object is equal to the product of its moment of inertia and its angular acceleration (? = I·?). This law is integral to linking the applied force (via torque) and the resulting angular acceleration.

Relationship between Angular and Linear Acceleration

The relationship between angular acceleration (?) and linear acceleration (a) is given by the equation a = ?·r, where r is the radius of the circular path. This concept is essential for connecting rotational motion with the linear motion of a point on the edge of a rotating object.

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