A playground carousel is rotating counterclockwise about its centeron frictionle

Question

A playground carousel is rotating counterclockwise about its centeron frictionless bearings. A person standing still on the groundgrabs onto one of the bars on the carousel very close to its outeredge and climbs aboard. Thus, this person begins with an angularspeed of zero and ends up with a nonzero angular speed, which meansthat he underwent a counterclockwise angular acceleration. Thecarousel has a radius of 1.50m, an initial angular speed of3.14rad/s, and a moment of inertia of 125kgm2, The massof the person is 40kg. Find the final angular speed of the carouselafter the person climbs aboard.

Explanation / Answer

    Moment of inertia of carousel, I1 = 125kgm^2     Mass of the person, M = 40 kg     Radius of the carousel, R = 1.5 m     Moment of inertia of the person, I2 = M R 2                                                         = 40 * 1.5 2                                                         = 90 kg m^2     Initial amgular velocity of carousel , =3.14 rad/s     Final angular velocity of carousel + person,' = ?     From law of conservation of angularmomentum,     ( I1 + I2 ) ' = I1     Final angular velocity of carousel + person,' = ( 125 * 3.14 ) / ( 125 + 90 )                                                                          = 1.83 rad/s

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