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Textbook Guide Physics: Momentum, Inertial Frame Of Reference, Wheel Slide Protection

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grayraven524
1 Dec 2016
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UTSG
Department
Physics
Course
PHY131H1
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all

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PHY131H1 Full Course Notes
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Document Summary

Rolling as translation and rotation combined: apply the relationship between the centre-of-mass speed and the angular speed of a body in smooth rolling. Rolling can be seen as a combination of translation and rotation. In ideal conditions, rolling will occur along completely smooth surfaces. The centre of mass o of a rolling wheel moves a distance s at velocity ~vcom while the wheel rotates through angle . This distance s is the linear translation of the wheel"s centre of mass. The linear speed vcom of the centre of the wheel (the centre of mass of a uniform wheel) is ds/dt. Its angular speed about the centre of the wheel is d /dt. The movement of any rolling object (such as a wheel) can be decomposed into combination of pure rotation and pure translation components. vcom = r. We can interpret the term 1 its axis through its centre of mass. The term 1 motion of the wheel"s centre of mass.

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Physics: Principles with Applications
7th Edition, 2013
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ISBN: 9780321625922

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Related Questions

With axle and spokes of negligible mass and a thin rim, a certain bicycle wheel has a radius of 0.39 m and weighs 33 N. It can turn on its axle with negligible friction. A man holds the wheel above his head with the axle vertical while he stands on a turntable that is free to rotate without friction. The wheel rotates clockwise, as seen from above, with an angular speed of 50.8 rad/s, and the turntable is initially at rest. The rotational inertia of wheel + man + turntable about the common axis of rotation is 2.1 kg·m2. The man's free hand suddenly stops the rotation of the wheel (relative to the turntable). Determine the resulting angular speed and direction of rotation of the system. (Include the sign. Take clockwise as seen from above to be positive.)

THIS QUESTION IS ROTATIONAL KINEMATICS
Q#1
(A) A wheel starts from rest and rotates about its axiswithconstant angular acceleration. after 6.8s have elapsed, ithasrotated through an angle of 25 radians. (a) what is theangularacceleration of the wheel?(b) what is the angular velocityofthe wheel when the t=6.8seconds?(c) what is thecentrepitalacceleration of a point on the wheel at a distance r=0.45m from the axis at t =6.8s?
(B) A pneumatic high speed cutter with a 7.50cmdiametercutting disc is advertizes to have a rotation rate ofbetween 5000and 18,000 rev/min. (a)what is range of angular speedin rad/s?(b)what is range of linear speed of the edge of the disc?(c) whatis the average angular acceleration, if starting from rest,thecutter comes up to its fastest speed in 2.8s?
(C) A car engine idles at 800rpm, with the car in nuetral,youdepress the accelerator. After 1.2 sec. the tachometerindicatoesan engine speed of 3400rpm.(a) what are the initialangularvelocities in rad/s? (b) what is the average angularaccelerationduring the 1.20s interval?(c) how many revolutions doesthe enginemake during that 1.20s?

I would appreciate help with any of the following problems. Thankyou.

22. In an isometric exercise a person places a hand on a scale andpushes vertically downward, keeping the forearm horizontal. This ispossible because the triceps muscle applies an upward forceperpendicular to the arm, as the figure indicates. The forearmweighs 22.1 N and has a center of gravity as indicated. The scaleregisters 113 N. Determine the magnitude of .
Distance between the force applied by the muscle and the elbowjoint 0.025 m. The distance between the elbow joint and the armscenter of gravity is 0.15 m. Distance between the arms center ofgravity and the center of the scale is 0.15 m. I was not able tofind the answer to this problem using the solution posted on thewebsite.

26.A wrecking ball (weight = 4310 N) is supported by a boom, whichmay be assumed to be uniform and has a weight of 2550 N. As thedrawing shows, a support cable runs from the top of the boom to thetractor. The angle between the support cable and the horizontal is32°, and the angle between the boom and the horizontal is 48°. Find(a) the tension in the support cable and (b) the magnitude of theforce exerted on the lower end of the boom by the hinge at pointP.

56. Two identical wheels are moving on horizontal surfaces. Thecenter of mass of each has the same linear speed. However, onewheel is rolling, while the other is sliding on a frictionlesssurface without rolling. Each wheel then encounters an inclineplane. One continues to roll up the incline, while the othercontinues to slide up. Eventually they come to a momentary halt,because the gravitational force slows them down. Each wheel is adisk of mass 3.64 kg. On the horizontal surfaces the center of massof each wheel moves with a linear speed of 5.26 m/s. (a),(b) Whatis the total kinetic energy of each wheel? (c), (d) Determine themaximum height reached by each wheel as it moves up the incline. Iwas able to solve for the rolling wheel but couldn't find the rightanswers for the sliding wheel.

66. A thin uniform rod is rotating at an angular velocity of 1.89rad/s about an axis that is perpendicular to the rod at its center.As the figure indicates, the rod is hinged at two places,one-quarter of the length from each end. Without the aid ofexternal torques, the rod suddenly assumes a "u" shape, with thearms of the "u" parallel to the rotation axis. What is the angularvelocity of the rotating "u"?

76. A woman who weighs 501 N is leaning against a smooth verticalwall, as the drawing shows. Find (a) the magnitude of the force N(directed perpendicular to the wall) exerted on her shoulders bythe wall and the (b) horizontal and (c) vertical components of theforce exerted on her shoes by the ground.