 Classical Mechanics

# 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 $$28.0\text{ rad/s}^2$$ is generated by a $$44.0\text{ N}\cdot\text{m}$$ 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 $$0$$ to $$5.35\text{ rad/s}$$ in $$190\text{ ms}.$$ If the rotational inertia about his center of mass is $$12.0\text{ kg}\cdot\text{m}^2,$$ 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 $$F_1=110\text{ N}$$ and $$F_2=70\text{ N}$$ are acting on it, as shown above. If the mass of the cylinder is $$100\text{ kg},$$ what is the rotational acceleration produced by the two forces? Two blocks of masses $$m_1=430\text{ g}$$ and $$m_2=500\text{ g}$$ 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 $$R=5.00\text{ cm}.$$ If they are released from rest, block $$m_2$$ falls $$48.0\text{ cm}$$ in $$4.00\text{ s}.$$ If there is no slippage between the cord and the pulley, what is the rotational inertia of the pulley?

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

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