Physics
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A cylinder is fixed on the top of a rotating platform. The angular velocity of the cylinder is shown as a function of time in the figure below. Calculate the number of rotations completed by the cylinder between 0 and 6 s.
A compact motor pulley is utilized to spin a large grinding disc. The pulley and disc are aligned so their outer rims make contact. The motor pulley, with a radius of 8.0 cm, accelerates at 8.0 rad/s² and remains in touch with a grinding disc that has a radius of 22.0 cm without experiencing any slippage. Determine what the grinding disc's angular acceleration value will be.
How long does it take for a large milling wheel to achieve a speed of 66 rpm when rotated by a small driving gear with a radius of 8.0 cm accelerating at 8.0 rad/s², given that the gear and wheel make contact without slipping and the wheel's radius is 22.0 cm?
What is the diameter of a soccer ball that rolls 3.2 m and makes 13.0 revolutions?