An electric motor rotating a workshop grinding wheel at 1.16 times 10^2 rev/min

Question

An electric motor rotating a workshop grinding wheel at 1.16 times 10^2 rev/min is switched off. Assume the wheel has a constant negative angular acceleration of magnitude 2.02 rad/s^2. a. How long does it take the grinding wheel to stop? b. Through how many radians has the wheel turned during the time interval found in part (a)? Spike is riding on a carousel and finds that he is feeling a bit nauseated. He then decides to move from the outer edge of the carousel to a point a distance r_2 from the center so that his linear speed is reduced by a factor of 2.5. If the carousel has a constant angular speed of 1.0 rad and a radius of 3.3 m, what is r_2? A model airplane with mass 0.749 kg is tethered to the ground by a wire so that it flies in a horizontal circle 30.6 m in radius. The airplane engine provides a net thrust of 0.796 N perpendicular to the tethering wire. a. Find the magnitude of the torque the net thrust produces about the center of the circle. b. Find the magnitude of the angular acceleration of the airplane. c. Find the magnitude of the tangential acceleration of the airplane. A disk 8.08 cm in radius rotates at a constant rate of 1, 260 rev/min about tis central axis. a. Determine its angular speed. b. Determine the tangential speed at a point 3.02 cm from its center. c. Determine the radial acceleration of a point on the rim. d. Determine the total distance a point on the rim moves in 2.04 s. Consider two objects with m_1 > m_2 connected by a light string that passes over a pulley having a moment of inertia of I about its axis of rotation as in the figure. The string does not slip on the pulley or stretch. The pulley turns without friction. The two objects are released from rest separated by a vertical distance 2h. Give your final answers using the following variables: g, R, h, m_1, m_2, and I. a. Use the principle of conservation of energy to find the translational speeds of the masses as they pass each other. b. Find the angular speed of the pulley at this time.

Explanation / Answer

1) a)

here by using the formula

w = w0 - alpha * t

0 = 116 * 2 * pie / 60 - 2.02 * t

t = 6 sec

b)

radians = w0 * t - 0.5 * alpha * t^2

= 116 * 2 * 3.14 * 6 / 60 - 0.5 * 2.02 * 6^2

= 36.48 radins

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