Questions are in the photos, see 4 attachments.

Post by **answerhappygod** » Sat Feb 26, 2022 11:49 am

Questions are in the photos, see 4

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attachments.

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H: Rolling Motion - Bicycle Wheel Bookmark this page You have a bicycle wheel of radius Rin non-slip rolling on a flat horizontal surface. The center of the wheel is moving to the +x direction with velocity vz. The point at the bottom of the wheel att = O is located at the origin; we will follow this special point. We will refer to the special point we are following as the point'. The +y direction is chosen upward. The motion of the wheel is a translation at velocity vz added to a clockwise rotation of an origin-centered wheel at angular velocity w, raised upward so the bottom of the wheel has y = 0. The diagram provides a conceptual overview of the decomposition of the rolling motion explained in the next five problems of the sequence. A + 4 + XL = אן
The 'Bicycle Wheel' sequence below is about finding the motion of a point on a wheel, the point initially at the bottom of the wheel, as a function of time, as the wheel rolls clockwise to the right on a horizontal surface. The motion is represented as the sum of three vectors. The vectors are a uniform circular motion on a circle centered at the origin, a lift by the displacement of the radius, and a translation to the right along the horizontal surface at the speed needed to simulate non-slip rolling along the surface. What does the fact vector addition is commutative allow us? Rotating Wheel at Origin 0.0/10.0 points (graded) Start with the wheel centered at the origin and rotating clockwise with angular velocity of magnitude w > 0. Att = 0 the point has position (0, -R) Using the coordinates already specified, calculate the position vector ēr = (xr(t), YR(t)) of the point on the rotating wheel (for the 'R' subscript think 'point on edge of rotating wheel at origin') as a function of time. Use the standard trigonometry convention for the direction of positive angle. Enter your responses in terms of some or all of v_x for Vg, t fort, R for R, and omega for w.
xr(t) = Yr(t) = SUBMIT You have used 4 of 10 attempts Save Translation of Lift 0.0/10.0 points (graded) Now add a constant vector displacement lift T L = (XL, YL) to position of the special point on the rotating wheel so that at time t = 0 the position of the special point is the origin. Determine the values of the lift displacement components. Enter your responses in terms of some or all of v_x for vz, t fort, R for R, and omega for w. XL(t) = YL (t) =
Translation Of Rolling 0.0/10.0 points (graded) YT Now add a vector displacement translation čr(t) = (xt(t), yr(t)) to the motion of the rotating wheel so that the center of the wheel moves to the +x direction with velocity vz. Enter the values of the translation displacement below. Enter your responses in terms of some or all of v_x for Vg, t fort, R for R, and omega for w. XT(t) = yr(t) = SUBMIT You have used 0 of 10 attempts Save
Point Position 0.0/10.0 points (graded) Finally, the position of the point on the rolling bicycle wheel in table-top motion is (t) = ēr(t) + (t) + r(t) = (x(t), y(t)). Calculate the components of the position of the point. Enter your responses in terms of some or all of v_x for vz, t fort, R for R, and omega forw. (t) = = g(t) SUBMIT You have used 0 of 10 attempts Save