Work-energy Theorem In Rotation

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A constant torque of 5 N·m acts on a wheel and turns it through an angular displacement of 8 radians about its fixed axis. How much rotational work is done by this torque on the wheel?

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NCERT Class 11, Chapter 7 (System of Particles and Rotational Motion) defines the work done by a constant torque during an angular displacement as W = τθ, which is the rotational analogue of the linear expression W = Fd. Here torque takes the place of force and the angular displacement in radians takes the place of linear distance. According to the work-energy theorem for rotation, this work equals the change in the body's rotational kinetic energy, so the wheel speeds up as the torque does positive work on it. Substituting the given values gives W = 5 × 8 = 40 J. The option 1.6 J results from dividing torque by angular displacement rather than multiplying them. The option 13 J comes from incorrectly adding the two quantities together. The option 3 J arises from subtracting one from the other. A dimensional check confirms that N·m multiplied by radians yields joules, since the radian is dimensionless, and 40 J is a reasonable amount of work for a 5 N·m torque acting through 8 radians. The positive sign of the result correctly indicates that energy is being added to the wheel's rotational motion.

Work-energy Theorem In Rotation

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