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Consider an amusement park ride in which participants are rotated about a vertical axis in a cylinder with vertical walls. Once the
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- An ultracentrifuge accelerates from to 100,000 rpm in 2.00 min. (a) What is the average angular acceleration in rad/s2 ? (b) What is the tangential acceleration of a point 9.50 cm from the axis of rotation? (c) What is the centripetal acceleration in m/s2 and multiples of g of this point at full rpm? (d) What is the total distance travelled by a point 9.5 cm from the axis of totation of the ultracentrifuge?arrow_forwardKeratinocytes are the most common cells in the skins outer layer. As these approximately circular cells migrate across a wound during the healing process, they roll in a way that reduces the frictional forces impeding their motion. (a) Given a cell body diameter of 1.00 105 m (10 m), what minimum angular speed would be required to produce the observed linear speed of 1.67 107 m/s (10 m/min)? (b) How many complete revolutions would be required for the cell to roll a distance of 5.00 103 m? (Because of slipping as the cells roll, averages of observed angular speeds and the number of complete revolutions are about three times these minimum values.)arrow_forwardWhy is the following situation impossible? A mischievous child goes to an amusement park with his family. On one ride, after a severe scolding from his mother, he slips out of his seat and climbs to the top of the rides structure, which is shaped like a cone with its axis vertical and its sloped sides making an angle of = 20.0 with the horizontal as shown in Figure P6.32. This part of the structure rotates about the vertical central axis when the ride operates. The child sits on the sloped surface at a point d = 5.32 m down the sloped side from the center of the cone and pouts. The coefficient of static friction between the boy and the cone is 0.700. The ride operator does not notice that the child has slipped away from his seat and so continues to operate the ride. As a result, the sitting, pouting boy rotates in a circular path at a speed of 3.75 m/s. Figure P6.32arrow_forward
- Unreasonable Results You are told that a basketball player spins the ball with an angular acceleration of 100 rad/s2. (a) What is the ball's final angular velocity if the ball stairs from rest and the acceleration lasts 2.00 s? (b) What is unreasonable about the result? (c) Which premises are unreasonable or inconsistent?arrow_forward(a) What is the period of rotation of Earth in seconds? (b) What is the angular velocity of Earth? (c) Given that Earth has a radius of 6.4106 m at its equator, what is the linear velocity at Earth's surface?arrow_forwardA particle moves 3.0 m along a circle of radius 1.5 m. (a) Through what angle does it rotate? (b) If the particle makes this trip in 1.0 s at a constant speed, what is its angular velocity? (c) What is its acceleration?arrow_forward
- A system of point particles is rotating about a fixed axis at 4 rev/s. The particles are fixed with respect to each other. The masses and distances to the axis of the point particles are m1=0.1kg , r1=0.2m , m2=0.05kg , r2=0.4m , m3=0.5kg , r3=0.01m . (a) What is the moment of inertia of the system? (b) What is the rotational kinetic energy of the system?arrow_forwardA bicyclist is testing a new racing bike on a circular track ofradius 53.0 m. The bicyclist is able to maintain a constant speedof 24.0 m/s throughout the test run. a. What is the angularspeed of the bike? b. What are the magnitude and direction ofthe bikes acceleration?arrow_forwardFriction in an old clock causes it to lose 1 minute per hour. Assume the angular acceleration is constant, the positive z axis points out of the face of the clock, and at the beginning of the hour it was at its ideal angular speed. Find the angular acceleration of the minute hand (long hand) and its angular velocity at the end of the hour.arrow_forward
- Suppose when Earth was created, it was not rotating. However, after the application of a uniform torque after 6 days, it was rotating at 1 rev/day. (a) What was the angular acceleration during the 6 days? (b) What torque was applied to Earth during this period? (c) What force tangent to Earth at its equator would produce this torque?arrow_forwardTwo bugs, Buzz and Crunchy, are siting on a spinning disk on a horizontal plane. Buzz is sitting halfway and Crunchy is sitting at the outer edge as shown. The radius of the disk is 0.80 m and the disk is rotating with an angular speed of 38 rpm. The coefficient of friction between the bugs and the disk are us = 0.80 and uk = 0.60. What is the magnitude of the friction force on Buzz, in Newtons? Buzz has a mass of 2.0 kg (I know, a big bug!). Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement. Crunchyarrow_forwardA skateboarder is attempting to make a circular arc of radius r = 16 m in a parking lot. The total mass of the skateboard and skateboarder is m = 91 kg. The coefficient of static friction between the surface of the parking lot and the wheels of the skateboard is μs = 0.69 . a)What is the maximum speed, in meters per second, he can travel through the arc without slipping? b) He speeds up very slightly and begins to slide. The coefficient of kinetic friction is μk = 0.24. What is the new magnitude of his radial acceleration in m/s2?arrow_forward
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