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Консультация № 173579
22.10.2009, 22:15
25.00 руб.
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Помогите пожалуйста уважаемые эксперты.
163. На краю горизонтальной платформы, имеющей форму диска радиусом
2 м, стоит человек. Масса платформы 200 кг, масса человека 80 кг. Платформа может вращаться вокруг вертикальной оси, проходящей через её центр. Пренебрегая трением, найти, с какой угловой скоростью будет вращаться платформа, если человек будет идти вдоль её края со скоростью 2 м/с относительно платформы.
163. На краю горизонтальной платформы, имеющей форму диска радиусом
2 м, стоит человек. Масса платформы 200 кг, масса человека 80 кг. Платформа может вращаться вокруг вертикальной оси, проходящей через её центр. Пренебрегая трением, найти, с какой угловой скоростью будет вращаться платформа, если человек будет идти вдоль её края со скоростью 2 м/с относительно платформы.
Обсуждение
23.10.2009, 00:50
общий
это ответ
Здравствуйте, Яна Владимировна.
момент инерции платформы J1=m1R2/2=400 кг/м2
человека - J2=m2R2=320 кг/м2
пусть платформа вращается с угловой скоростью [$969$]1, а радиус-вектор от центра платформы к человеку (в инециальной системе отсчёта) - со скоростью [$969$]2 (в противоположном направлении)
согласно закону сохранения момента импулься J1[$969$]1=J2[$969$]2
[$969$]2/[$969$]1=400/320=1,25
С другой стороны, угловая скорость человека (точнее, направленного на него радиус-вектора) относительно платформы равна [$969$]1+[$969$]2=v/r=1 рад/с
2,25[$969$]1=1 рад/с
[$969$]1=0,4 рад/с
момент инерции платформы J1=m1R2/2=400 кг/м2
человека - J2=m2R2=320 кг/м2
пусть платформа вращается с угловой скоростью [$969$]1, а радиус-вектор от центра платформы к человеку (в инециальной системе отсчёта) - со скоростью [$969$]2 (в противоположном направлении)
согласно закону сохранения момента импулься J1[$969$]1=J2[$969$]2
[$969$]2/[$969$]1=400/320=1,25
С другой стороны, угловая скорость человека (точнее, направленного на него радиус-вектора) относительно платформы равна [$969$]1+[$969$]2=v/r=1 рад/с
2,25[$969$]1=1 рад/с
[$969$]1=0,4 рад/с
5
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