Moving Reference Frame Kinematics Homework

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1 Chapter 3 Moving Reference Frame Kinematics Homework Freeform c

2 3-2 Freeform c 2018

3 Homework H.3. Given: The disk shown is rotating about its center with a constant rotation rate of Ω. Four slots have been cut into the disk, and a particle in each slot has a constant speed of v rel relative to the disk. Each particle is at a distance of R from the center of the disk. Find: Determine the velocit and acceleration of each particle in the disk. Write our answers as vectors. v rel v rel v rel R D v rel C θ Ω Freeform c

4 Homework H.3. Given: n L-shaped telescoping arm is pinned to ground at point. End of the arm is constrained to move within a stationar circular slot with a constant speed of v. t the instant shown, the arm is oriented horizontall with end located immediatel to the left of the center C of the circular slot. set of z aes are attached to section of the telescoping arm, with an observer also attached to this section of the arm. Find: Determine the angular velocit and angular acceleration of the arm. Write our answers as vectors. h R C v b 3-4 Freeform c 2018

5 Homework H.3.C Given: rm D is made from a quarter circular arc bar of radius R and is pinned to fied ground at end. Slotted arm E is pinned to fied ground at end with pin located directl below pin, as shown. pin at end D of the curved arm is allowed to slide within the slot of arm E. t the position shown, arm E is horizontal, and arm D is rotating CW with a constant rate of ω D. Find: For this position, (a) Determine the angular velocit of arm E and the value of d. (b) Determine the angular acceleration of arm E and the value of d. HINT: Use an observer attached to the slotted arm E, and relate the kinematics of points and D through the moving reference frame kinematics equations. ω D R D d E Freeform c

6 Homework H.3.D Given: guide rod is able to control the angular position of the L-shaped arm E through its end moving verticall and through the slot cut into section E of the arm. In turn, arm E controls the horizontal position of slider C through end being constrained to move within the slot in slider C. For a particular task of this mechanism, end of the guide rod is moving upward with a constant speed v. ur goal is to determine the velocit and acceleration of slider C. Find: For this problem: (a) Determine the angular velocit and angular acceleration of arm E. (b) Determine the velocit and acceleration of pin on E. (c) Determine the velocit and acceleration of slider C. HINT: Consider using an observer attached to the slotted arm E. C L θ d v E θ Use the following parameters in our analsis: v = 20 ft/s, θ = 30, L = 2 ft and d = 1.5 ft. 3-6 Freeform c 2018

7 instant when " = 0, bar is being raised at a rate of 4 rad/sec from the horizontal plane. In addition, the rate at which the bar is being raised is decreasing at a rate 3 rad / sec 2. Chapter 3: Moving Reference Frame Kinematics Homework set of z coordinate aes is attached to bar with its origin at. second set of coordinate aes, YZ, are fied to ground. t the instant when " Homework = 0, H.3.E the z and YZ aes are aligned with each other. Given: shaft rotates about a fied vertical ais at a constant rate of Ω, as shown below. Find: For the instant when " = 0: straight bar, having a length of L, is pinned to point on the shaft, with being on the rotation ais of a) the find shaft. the angular t the instant velocit when and angular θ = 0, bar acceleration is being raised at a rate of θ from the horizontal plane, with this rate changing at a rate of θ. of bar. set of z coordinate aes is attached b) find the acceleration of point on the bar. to bar with its origin at. second set of coordinate aes, Y Z, are fied to ground. t the instant when θ = 0, the z and Y Z aes are aligned with each other. ll answers should be epressed in vector form. You ma choose to write these vectors in Find: terms For of either the instant their z when or YZ θ = 0 components., determine the angular velocit and angular acceleration of bar. Y L " bar vertical shaft! bearing Use the following parameters in our analsis: Ω = 5 rad/s, θ = 4 rad/s, θ = -3 rad/s 2 and L = 2 m. Freeform c

8 Homework H.3.F Given: shaft is rotating at a constant rate of Ω about a fied ais. disk of radius R is able to roll without slipping in a slot that is cut longitudinall into the shaft. The position of the disk s center is controlled b an hdraulic clinder that is etending at a constant rate of d. Consider a set of coordinate aes z that are attached to the disk, and a set of coordinate aes Y Z that are fied in space. Find: For this problem, (a) determine the angular velocit and angular acceleration of the disk. (b) determine the acceleration of point on the perimeter of the disk at a time when is immediatel to the right of, as shown in the figure. Y d R R no slip Ω 3-8 Freeform c 2018

9 Homework H.3.G Given: The oke shown below rotates about a fied ais with a constant rate of ω 0. disk, of radius r, rotates about its center C at a constant rate of ω disk relative to oke. The Y Z coordinate sstem is fied with the -ais aligned with the fied rotation ais of the oke. The z coordinate sstem is attached to the disk with the z-ais aligned with the rotation ais of the disk for all time. For the position shown below, the z aes are aligned with the Y Z aes. Find: For the position shown: (a) Determine the angular velocit and angular acceleration of the disk. Write our answers as vectors in terms of their z components. (b) Determine the acceleration of point of the disk. Write our answer as a vector in terms of its z components. C disk z r C disk 0 0 Z Y d b left view front view Use the following parameters in our analsis: ω 0 = 3 rad/s, ω disk = 2 rad/s, d = 0.5 m, b = 1.5 m and r = 0.25 m. Freeform c

10 Homework H.3.H Given: caster wheel is supported b an L-shaped bracket. The bracket is rotating about a fied vertical ais with a constant rate of ω 1. The wheel rotates with respect to the bracket with a constant rate of ω 2. Find: For this problem, determine: 1. The angular velocit and angular acceleration of the wheel. Write our answers as vectors. 2. The acceleration of point on the wheel at the instant shown when is immediatel to the right of the center of the wheel. 3. The acceleration of point on the wheel at the instant shown when is immediatel above the center of the wheel. ω 1 ω 2 r d Use the following parameters in our analsis: ω 1 = 2 rad/s, ω 2 = 5 rad/s, r = 200 mm and d = 100 mm Freeform c 2018

11 ference Frame Kinematics Homework Problems ME 274 Homework H.3.I m III-23 particle P Given: travels in Particle a tube Pwith travels R = 6in ft a/sec tube= with constant Ṙ =. The constant. tube is The being tube is being raised at a constant raised at a constant rate of θ. rate In of addition,! = 3 rad the/sec tube. In isaddition, attachedthe to atube vertical is attached shaft which to a is rotating about the fied Y vertical shaft ais which withis a rotating constantabout rate of the ω. fied n observer Y ais with is attached a constant to the rate tube of with the z aes also attached! = 4 rad /sec to the. n tube observer with its is attached origin atto point the tube. with the z aes also attached to the tube with its origin at point. Find: For the position shown, determine: You are asked (a) to The find angular the acceleration velocit vector of particle of thep observer. when R = 5 feet and! = In doing so, answer the following questions. (b) The angular acceleration vector of the observer. a) Find the angular velocit vector of the observer. b) Find (c) the angular The velocit acceleration of point vector P as seen of the b observer. the observer. c) What (d) is the The velocit acceleration of point of P point as seen P asb seen the b observer? the observer. d) What is the acceleration of point P as seen b the observer? (e) The acceleration of point P using the above results. e) Using the results from a)-d) above, find the acceleration of point P. Y R P! " Use the following parameters in our analsis: R = 5 ft, θ = 36.87, Ṙ = 6 ft/s, θ = 3 rad/s and ω = 4 rad/s. Freeform c

12 Homework H.3.J Chapter 3: Moving Reference Frame Kinematics Homework Given: shaft is rotating about the fied -ais at a constant rate of Ω. square plate is pinned at its center to the centerlineb of the shaft and is rotating relative to the shaft about at a constant rate of θ. set of z aes are attached to the plate with! b its origin at. n insect on the plate is walking along the -ais with a constant speed of v rel relative to the plate. Find: Determine the velocit and acceleration of the insect when the insect has reached the edge of the plate. The insect reaches the edge of the plate when θ = 0.! Y P v rel! b! b Use the following parameters in our analsis: b = 6 in, v rel = 12 in/s, Ω = 3 rad/s and θ = 5 rad/s Freeform c 2018

Moving Reference Frame Kinematics Homework

Chapter 3 Moving Reference Frame Kinematics Homework Freeform c 2016 3-1 3-2 Freeform c 2016 Homework 3. Given: n L-shaped telescoping arm is pinned to ground at point. The arm is rotating counterclockwise