Classical Mechanics

Moment of Inertia

Rotational Form of Newton's Second Law

         

I assume that you work through these problems using some sort of writing utensil. Take your pen, balance it on its tip, and let go. It falls over. How fast in m/s is the other end of the pen going when it hits the table, assuming the tip doesn't slip? Take the pen to be a uniform one dimensional rod of length 15 cm.

If an angular acceleration of 28.0 rad/s228.0\text{ rad/s}^2 is generated by a 44.0 Nm44.0\text{ N}\cdot\text{m} torque on a wheel, then what is the wheel's approximate rotational inertia?

Consider a diver who is launching from a diving board. When he launches from the board, his angular speed about his center of mass is changing from 00 to 5.35 rad/s5.35\text{ rad/s} in 190 ms.190\text{ ms}. If the rotational inertia about his center of mass is 12.0 kgm2,12.0\text{ kg}\cdot\text{m}^2, what is the magnitude of average external torque on him from the board during the launch?

A cylinder is pinned at its center and two forces F1=110 NF_1=110\text{ N} and F2=70 NF_2=70\text{ N} are acting on it, as shown above. If the mass of the cylinder is 100 kg,100\text{ kg}, what is the rotational acceleration produced by the two forces?

Two blocks of masses m1=430 gm_1=430\text{ g} and m2=500 gm_2=500\text{ g} are hanging on a pulley, as shown in the above figure. The pulley is fixed on a horizontal axle with negligible friction, and its radius is R=5.00 cm.R=5.00\text{ cm}. If they are released from rest, block m2m_2 falls 48.0 cm48.0\text{ cm} in 4.00 s.4.00\text{ s}. If there is no slippage between the cord and the pulley, what is the rotational inertia of the pulley?

The gravitational acceleration is g=9.8 m/s2.g=9.8\text{ m/s}^2.

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