A wheel can rotate about a fixed horizontal axis

PHYSICS · Subjective · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion

Problem

A wheel can rotate about a fixed horizontal axis. The sense of the positive angular displacement is taken to be counter-clockwise. (i) Define angular velocity and angular acceleration, mentioning the SI units of each. (ii) A student writes the kinematic relation ω=ω0+αt\omega = \omega_0 + \alpha t for a wheel that is initially spinning clockwise. Explain how the chosen sign convention changes the algebraic signs of ω0\omega_0 and α\alpha when the wheel is retarding while still spinning clockwise. (iii) Using the same relation, explain qualitatively the two different ways in which a wheel that starts with ω0<0\omega_0<0 can reach ω=0\omega = 0. Under what general condition (in terms of ω0, α,\omega_0,\,\alpha, and tt) will the wheel actually reverse its direction of rotation?

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