A grindstone has a moment of inertia of 6 kg m^2. A constant torque is applied and the grindst

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A grindstone has a moment of inertia of 6 kg m^2. A...

A grindstone has a moment of inertia of $6 \mathrm{~kg} \mathrm{~m}^{2}$. A constant torque is applied and the grindstone is found to have a speed of $150 \mathrm{rpm}, 10$ seconds after starting from rest. The torque is (a) $3 \pi \mathrm{Nm}$ (b) $3 \mathrm{~N} \mathrm{~m}$ (c) $\frac{\pi}{3} \mathrm{~N} \mathrm{~m}$ (d) $4 \pi \mathrm{N} \mathrm{m}$

A grindstone has a moment of inertia of $6 \mathrm{~kg} \mathrm{~m}^{2}$. A constant torque is applied and the grindstone is found to have a speed of $150 \mathrm{rpm}, 10$ seconds after starting from rest. The torque is
(a) $3 \pi \mathrm{Nm}$
(b) $3 \mathrm{~N} \mathrm{~m}$
(c) $\frac{\pi}{3} \mathrm{~N} \mathrm{~m}$
(d) $4 \pi \mathrm{N} \mathrm{m}$

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Key Concepts

Moment of Inertia

Moment of inertia is a measure of an object’s resistance to changes in its rotational motion. It depends on both the mass of the object and how that mass is distributed with respect to the axis of rotation, analogous to mass in linear motion.

Newton's Second Law for Rotation

This law relates the net torque applied to a rotating object to its moment of inertia and the resulting angular acceleration through the equation ? = I?. It serves as the rotational counterpart to F = ma in linear dynamics.

Angular Acceleration

Angular acceleration is the rate at which the angular velocity of an object changes with time. It is directly influenced by the applied torque and inversely proportional to the object's moment of inertia.

Angular Velocity Conversion

Angular velocity conversion involves translating rotational speed from one unit to another, such as from revolutions per minute (rpm) to radians per second (rad/s). Knowing that one revolution is 2? radians and one minute is 60 seconds is crucial for accurate calculations in rotational dynamics.

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