\( 00210.0 \) points A solid ball with a mass of \( 2.11 \mathrm{~kg} \) and a radius of \( 0.051 \mathrm{~m} \) starts from rest at the top of a \( 89.1^{\circ} \) slope with a vertical height of \( 3.20 \) \( \mathrm{m} \). It proceeds to roll without slipping down the slope. What is the translational speed of the ball when it reaches the bottom? The acceleration of gravity is \( 9.81 \mathrm{~m} / \mathrm{s}^{2} \). Answer in units of \( \mathrm{m} / \mathrm{s} \).
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A 2.00-kg solid, uniform ball of radius 0.100 m is released from rest at point A in Figure P8.59, its center of gravity a distance of 1.50 m above the ground. The ball rolls without slipping to the bottom of an incline and back up to point B where it is launched vertically into the air. The ball rises to its maximum height $h_{\max }$ at point $\mathrm{C}$ At point $\mathrm{B},$ find the ball's (a) translational speed $v_{\mathrm{B}}$ and $(\mathrm{b})$ rotational speed $\omega_{\mathrm{B}}$ . At point $\mathrm{C},$ find the ball's (c) rotational speed $\omega_{\mathrm{C}}$ and (d) maximum height $h_{\max }$ of its center of gravity.
A solid ball of mass $M$ and radius $R$ starts at rest at height $h$ above the bottom of the path in Fig. $10.26 .$ It rolls without slipping down the left side. The right side of the path, starting at the bottom, is frictionless. To what height does the ball rise on the right?
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