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ROTATIONAL MOTION REVIEWTerms:Law of Universal GravitationUniform circular motionPerceived weightCentripetal forceCentrifugal “force”Centripetal accelerationRotational MotionAngular displacementArc lengthAngular velocityPeriodFrequencyTangential speedAngular accelerationTangential accelerationTorqueRadial lineLine of actionMoment armRotational equilibriumCenter of gravityCenter of massMoment of inertiaAngular momentumConservation of angular momentumConceptual Questions:When using a lever, is it best to have the fulcrum closer to the load, closer to where you apply the force, or right down the middle? Why?To minimize the amount of force necessary to open a door, where should you push? Closer to the hinges or further? Why?On a balanced seesaw, a boy 4x heavier than his counterpart should sit _____ the distance from the fulcrum.Big trucks often have large steering wheels. Why would this be the case?Do walking or throwing a ball involve torque? Explain.208597525019000Which force will make the net torque equal zero? What does it mean when the net torque is zero?Which force will provide the largest positive torque? Largest negative torque?1676400635000Explain what translational equilibrium means. Explain what rotational equilibrium means. Can you have one without the other?Why is it easier to hold a long stick horizontally at its midpoint rather than at its end? Position a stick horizontally so that it rests on your two outstretched fingers held about 2 ft apart. Now slowly move your fingers toward one another. Observe the movement of the stick over your fingers: why does it alternate, sliding first over one finger and then the other? What is the significance of the point where your fingers finally meet? (Grab a meter stick and give it a try)A ball rolls around a circular track with an angular velocity of 4π rad/s. What is the period of the motion?2346706838200Rasheed and Sofia are riding a merry-go-round that is spinning steadily (see above). Sofia is twice as far from the axis as is Rasheed. Sofia’s angular velocity is ______ that of Rasheed.475297517335500Rasheed and Sofia are riding a merry-go-round that is spinning steadily. Sofia is twice as far from the axis as is Rasheed. Sofia’s speed is ______ that of Rasheed.Two coins rotate on a turntable. Coin B is twice as far from the axis as coin A.The angular velocity of A is twice that of BThe angular velocity of A equals that of BThe angular velocity of A is half that of BThe fan blade is slowing down. What are the signs of ω and α?398640316256000ω is positive and is positive. ω is positive and is negative. ω is negative and is positive. ω is negative and is negative. ω is positive and is zero.The fan blade is speeding up. What are the signs of and ? is positive and is positive. is positive and is negative. is negative and is positive. is negative and is negative. 745490143510This is the angular velocity graph of a wheel. How many revolutions does the wheel make in the first 4 s?Starting from rest, a wheel with constant angular acceleration spins up to 25 rpm in a time t. What will its angular velocity be after time 2t?Starting from rest, a wheel with constant angular acceleration turns through an angle of 25 rad in a time t. Through what angle will it have turned after time 2t?When a rigid object rotates about a fixed axis, what is true about all the points in the object? (There could be more than one correct choice.) They all have the same angular speed.They all have the same tangential speed.They all have the same angular acceleration.They all have the same tangential acceleration.They all have the same radial acceleration.Five forces act on a rod that is free to pivot at point P, as shown in the figure. Which of these forces is producing a counter-clockwise torque about point P? (There could be more than one correct choice.)1514475889000447675035242500The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left), or a distance r/2 from the axis of rotation (right). If you release the hanging blocks simultaneously from rest, which one hits the ground first?1047750495935The figure shows scale drawings of four objects, each of the same mass and uniform thickness, with the mass distributed uniformly. Which one has the greatest moment of inertia when rotated about an axis perpendicular to the plane of the drawing at point P?Problems:A chicken is running in a circular path with an angular speed of 1.52 rad/s. How long does it take the chicken to complete one revolution?At a certain instant, a compact disc is rotating at 210 rpm. What is its angular speed in rad/s?When a fan is turned off, its angular speed decreases from 10 rad/s to 6.3 rad/s in 5.0 s. What is the magnitude of the average angular acceleration of the fan?A bicycle wheel has an outside diameter of 66 cm. Through what distance does a point on the rim move as the wheel rotates through an angle of 70°?When Mary is 3.00 m from the center of a merry-go-round, her tangential speed is a constant 1.88 m/s.What is her angular speed in rad/s?What is the magnitude of her linear (tangential) acceleration?A child is riding a merry-go-round that is turning at 7.18 rpm. If the child is standing 4.65 m from the center of the merry-go-round, how fast is the child moving?A wheel accelerates from rest to 59 rad/s at a uniform rate of 58 rad/s2. Through what angle (in radians) did the wheel turn while accelerating?4076700324485In the figure, point P is on the rim of a wheel of radius 2.0 m. At time t = 0, the wheel is at rest, and P is on the x-axis. The wheel undergoes a uniform counterclockwise angular acceleration of 0.010 rad/s2 about the center O.At time t = 0, what is the tangential acceleration of P?What is the linear speed of P when it reaches the y-axis?What is the magnitude of the net linear acceleration of Pwhen it reaches the y-axis?How long after starting does it take for P to return to itsoriginal position on the x-axis?A centrifuge in a medical laboratory rotates at a rotational speed of 3600 rev/min. When switched off, it makes 50 complete turns at a constant angular acceleration before coming to rest.What was the magnitude of the angular acceleration of the centrifuge as it slowed down?How long did it take for the centrifuge to come to rest after being turned off?A man in a gym is holding an 8.0-kg weight at arm's length, a distance of 0.55 m from his shoulder joint. What is the torque about his shoulder joint due to the weight if his arm is horizontal?A man in a gym is holding an 8.0-kg weight at arm's length, a distance of 0.55 m from his shoulder joint. What is the torque about his shoulder joint due to the weight if his arm is held at 30° below the horizontal?471487518097500The figure shows a person's foot. In that figure, the Achilles tendon exerts a force of magnitude F = 720 N. What is the magnitude of the torque that this force produces about the ankle joint?While working with precision components, especially out in space, it is often necessary to use a torque wrench, a device that allows the user to exert only a pre-set amount of torque. Having dialed in a value of only 30 N·m, what maximum perpendicular force should be exerted on the handle of a wrench 25.0 cm from the bolt?A 50-kg boy and a 40-kg girl sit on opposite ends of a 3-meter see-saw. How far from the girl should the fulcrum be placed in order for the boy and girl to balance on opposite ends of the see-saw? ................
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