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?
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- A rotating table, with moment of inertia 29 kg·m2, is spinning at 40 rpm. A piece of clay is dropped onto the table, where it sticks a distance 1.2 m from the rotational axis. If the final angular speed of the rotating table and clay is 32 rpm, what is the mass of the clay?An amusement park ride rotates around a fixed axis such that the angular position of a point on the ride follows the equation: θ(t) = a + bt2 – ct3 where a = 1.9 rad, b = 0.75 rad/s2 and c = 0.025 rad/s3.Randomized Variables a = 1.9 radb = 0.75 rad/s2c = 0.025 rad/s3 1) What is the magnitude of the angular displacement of the ride in radians between times t = 0 and t = t1? 2) Determine an equation for the angular acceleration of the ride as a function of time, α(t). Write your answer using the symbols a, b, and c, instead of their numerical values. 3) What is the angular acceleration in rad/s2 when the ride is at rest at t = t1?A single-engine helicopter has two rotors; a main rotor and a tail rotor. The main rotor has a diameter of 15.4 m and rotates at the rate of 420 rev/min while the tail rotor with a diameter of 1.68 m rotates at 4000 rev/min. what are the speeds, in m/s, of the tips of each rotor? main rotor speed m/s tail rotor speed m/s
- A solid sphere is released from the top of a ramp that is at a height h1 = 2.45 m. It rolls down the ramp without slipping. The bottom of the ramp is at a height of h2 = 2.14 m above the floor. The edge of the ramp is a short horizontal section from which the ball leaves to land on the floor. The diameter of the ball is 0.13 m. a) Through what horizontal distance d, in meters, does the ball travel before landing? b)How many revolutions does the ball make during its fall?One end of a meter stick is pinned to a table, so the stick can rotate freely in a plane parallel to the tabletop. Two forces, both parallel to the tabletop, are applied to the stick in such a way that the net torque is zero. The first force has a magnitude of 2.00 N and is applied perpendicular to the length of the stick at the free end. The second force has a magnitude of 6.00 N and acts at a 38.9° angle with respect to the length of the stick. Where along the stick is the 6.00-N force applied? Express this distance with respect to the end of the stick that is pinned. d= i >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?
- 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 0.745 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 40.5 rpm. Neglecting the mass of the professor, how far are the weights from the rotational axis after she pulls her arms in? distance: about us careers privacy policy terms of use contact us help tv W MacBook Air 8828A 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?Your roommate is working on his bicycle and has the bike upside down. He spins the 56.0 cmcm -diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second. What is the pebble's acceleration? Express your answer with the appropriate units.
- Torque You are playing with the masking tape that came in your lab box. This tape has a thickness that is not small compared to the radius. You measure it and it has an outer radius of 6.40 cm and an inner radius of 3.95 cm. You weigh the tape roll and find that it has a mass of 79.5 g. Now you roll the tape like you would a hoop (Rolling tape 1 (00:05)). The video illustrates the idea of the motion - please do NOT use it for numerical values. You find that the tape starts from rest, and has a torque applied when you push on it with your finger. You push on the outer edge (perpendicular to the radial direction). This causes the tape to accelerate. After 0.75 seconds, you find that the tape has an angular velocity of 53.0 rpm (rotations / minute). What is the Force you applied to the tape to start the rotation? Your answer should have the following: 2 Decimal Places Correct SI Units Appropriate Signs for Vector quantity answers Answers must be in the following format: Written out and…A variation of the amusement park ride discussed in Problem 11 is the Gravitron, which consists of a rotating cylinder, where riders stand with their backs against the inner surface of the cylinder (see image). As the cylinder rotates faster, riders get stuck to the wall. The effect is great enough, that in some rides, the floor even drops away. Let’s model the Gravitron as a rotating cylinder with vertical walls. The radius of the cylinder is 5.5 m. At one point during the ride, the speed of the Gravitron is 24 rpm, at which point a rider slides down the wall at constant speed. What is the coefficient of kinetic friction between the rider and the wall?a bucket of water with a mass of 25 kilograms is lifted from a well by a rope which is wound around a cylinder with a radius of 0.10 meters. A 0.50 meter crank is attached to the cylinder so that it wraps the rope around the cylinder. what is the minimum force that must be applied to the crank to lift the water bucket ?