A three-blade wind turbine, which spins perpendicularly to the ground, is set on a pole that is 38 m tall and completes 5 revolutions in one minute. The length of one blade is approximately 4 m long. One particular blade lies parallel to the ground before the turbine started to spin.
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A three-blade wind turbine, which spins perpendicularly to the ground, is set on a pole that is 38 m tall and completes 5 revolutions in one minute. The length of one blade is approximately 4 m long. One particular blade lies parallel to the ground before the turbine started to spin.
b) What is the height of the tip of the blade after one second from start?

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- A professor sits on a rotating stool that is spinning at 10.0 rpm while she holds a heavy weight in each of her hands. Her outstretched hands are 0.795 m from the axis of rotation, which passes through her head into the center of the stool. When she symmetrically pulls the weights in closer to her body, her angular speed increases to 20.5 rpm. Neglecting the mass of the professor, how far are the weights from the rotational axis after she pulls her arms in?There is a clever kitchen gadget for drying lettuce leaves after you wash them. It consists of a cylindrical container mounted so that it can be rotated about its axis by turning a hand crank. The outer wall of the cylinder is perforated with small holes. You put the wet leaves in the container and turn the crank to spin off the water. The radius of the container is 12.2 cm. When the cylinder is rotating at 2.45 revolutions per second, what is the magnitude of the centripetal acceleration at the outer wall? Number Units #The diameters of the main rotor and tail rotor of a single-engine helicopter are 7.59 m and 0.98 m, respectively. The respective rotational speeds are 456 rev/min and 4143 rev/min. a) Calculate the speeds of the tips of both rotors. b) Compare these speeds with the speed of sound, 343 m/s.
- 3. A telephone pole has been knocked over by the wind so that it makes an angle of 0 with the vertical. The wind has stopped blowing and the pole is to be cut down as shown. nail L cut Once the cut is across most of the thickness of the pole, the pole begins to tip over. As the pole tips, the bottom of the pole stays attached to the base by the remaining part of the pole that was not cut (but the torque from the base on the tipping pole is negligible). There is a nail (of negligible mass) on the pole located a distance x. The length of the pole from the cut to the top is L. Remember that the moment of inertia of a stick of mass m and length L about its end is mL?.A turntable 46.0 cm in diameter diameter starts from rest, and rotates at 68.0 rpm at its first complete revolution with constant angular acceleration. If it maintains the same acceleration, a) what is the rotational speed at time 34.0 seconds? b) what is the tangential speed of a point 10 cm from the edge of the turntable at time 34.0 seconds?A ship's wheel can be approximated as an annular cylinder (different from a ring) of mass 6.7 kilograms, inner radius 25 centimeters, and outer radius 32 centimeters; and eight spokes of mass 0.50 kilograms and length 49 centimeters. a. What is the moment of inertia? Include units in your answer. More information. b. Disagreeing over which way to go, the captain and the helmsman try to turn the wheel in opposite directions. The captain applies a force of 311 newtons at the inner radius, while the helmsman applies a force of 287 newtons at the outer radius. What is the magnitude of the angular acceleration of the wheel? Include units in your answer.
- An athlete with a mass of 62.0 kg is rotating head-over-heels in mid-air, at an angular speed of 2.00 revolutions per second, in a tucked position (that is, with arms, legs, and head pulled into a tight ball). In this position, the athlete can be modeled as a solid sphere with a radius of 0.500 m, rotating about its center. Just before landing, while still in the air, the athlete fully extends her arms and legs. In this position, she can be modeled as a long, thin rod, with a length of 1.80 m, the distance from her feet to her fingertips. The rod rotates about the center, with the axis of rotation perpendicular to the length of the rod. What is her angular speed (in revolutions per second) with her arms and legs fully extended?A three-blade wind turbine, which spins perpendicularly to the ground, is set on a pole that is 38 m tall and completes 5 revolutions in one minute. The length of one blade is approximately 4 m long. One particular blade lies parallel to the ground before the turbine started to spin. a) What is the equation that models the height of tip of this blade as a function of time (in seconds)?A “blink of an eye” is a time interval of about 150 ms for an average adult. The “closure” portion of the blink takes only about 55 ms. Let us model the closure of the upper eyelid as uniform angular acceleration through an angular displacement of 12.2°. A) What is the value of the angular acceleration the eyelid undergoes while closing? in rad/s^2 B) What is the tangential acceleration of the edge of the eyelid while closing if the radius of the eyeball is 1.25 cm? in m/s^2
- A child jumps to the edge of a carousel, that is in the shape of a circular plate with a radius of 1.3 m and was rotating at an angular velocity of 1.2 s-1 before the chuld jumped on it. The weight of the carousels is 80 kg, the weight of the child is 22 kg. What is their angular velocity after the jump? Later, the child moves closer to the center of the carousel plate by 80 cm. What is the new angular velocity?At it's peak, a tornado is 75m in diameter and carries 470m/s wind at its outer edge. What is it's angular speed in radians per second?Wile E. Coyote wants to flatten the Road Runner. Wile E. puts food at a pre-determined distance from the edge of a cliff. While the Road Runner eats the food, Wile E. pushes a log down the hill. It rolls without slipping. The radius of the log is 0.3 m. The mass of the log is 80 kg. The rotational inertia of the log is given by I = ½ MR2 . The translational speed of the log just before it leaves the cliff horizontally is 16 m/s. The Road Runner is 10 m below the cliff. If the log is to successfully hit the Road Runner, the food must be place at a precise location from the base of the cliff which you will determine. a. Use only energy considerations and the fact that the log does not slip as it rolls to determine the height it started from, h, before it went over the cliff. b. Determine how far from the edge of the cliff the food needs to be placed so the log lands on the Road Runner. The rotating motion of the log in the air does not affect the motion of the log once it is in the air.…