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 with a constant rotation rate of θ and is etending at a rate of L. set of z aes are attached to section B of the telescoping arm, with an observer also attached to this section of the arm. Find: For this problem: (a) Determine the velocit and acceleration of end. Write our answers as vectors. (b) Determine the rate of change of speed of and the radius of curvature for the path of. Y L h B θ X Use the following parameters in our analsis: h = 4 in, b = 10 in, L = 24 in, θ = 2 rad/s, L = 5 in/s and L = 0 in/s 2. Freeform c 2016 3-3
Homework 3.B Given: rm D rotates about point with a constant rate of θ. belt slides around the perimeter of the arm with a constant speed of v rel relative to the arm. Find: For this problem: (a) Determine the acceleration of point on the belt. Write our answer as a vector. (b) Determine the acceleration of point B on the belt. Write our answer as a vector. belt d d point B r D point rotating arm v rel θ Use the following parameters in our analsis: d = 100 mm, r = 20 mm, v rel = 100 mm/s and θ = 2 rad/s. 3-4 Freeform c 2016
Homework 3.C Given: Rod B is able to slide through collar at D as the slider at moves along a horizontal surface with a constant speed of v. n observer also attached to the collar. Find: For this problem: (a) Determine the angular velocit and angular acceleration of rod B. Write our answers as vectors. (b) Determine values for L and L. B d L D θ v Use the following parameters in our analsis: d = 0.5 ft, θ = 36.87 and v = 8 ft/s. Freeform c 2016 3-5
Homework 3.D Given: Bar CD is pinned to ground at end. straight slot is cut into section CD of bar CD, as shown. Pin B on link B is allowed to slide relative to the slot. Link B is rotating in the counterclockwise direction with a constant angular speed of ω B. t the position shown, section C of CD is horizontal and the slot in section CD of CD is vertical. n observer and a set of z aes are attached to bar CD. Find: For this position, determine the angular velocit and angular acceleration of bar CD. Write our answers as vectors. D b B!! B d L C Use the following parameters in our analsis: θ = 36.87, L = 4 ft, d = 3 ft, b = 2 ft, ω B = 4 rad/s. 3-6 Freeform c 2016
Homework 3.E Given: disk and shaft C are mounted in a clevis that rotates about a fied vertical ais at a rate of ω 0. The shaft and disk rotate with respect to the clevis with a rate of ω disk in the direction shown below, with the angle θ held constant. The XY Z coordinate sstem is fied with the Y -ais aligned with the fied rotation ais of the clevis. The z coordinate sstem is attached to the disk with the -ais aligned with C for all time. For the position shown below, the z- and Z-aes are aligned. Find: For the position shown: (a) Determine the angular velocit of the disk. Write our answer as a vector in terms of its z components. (b) Determine the angular acceleration of the disk. Write our answer as a vector in terms of its z components. Y Z disk X C z disk 0 Use the following parameters in our analsis: θ = 36.87, ω 0 = 4 rad/s = constant and ω disk = 6 rad/s = constant. Freeform c 2016 3-7
Homework 3.F Given: disk and shaft C are mounted in a clevis that is attached to a fied vertical ais such that ω 0 = 0 rad/s. The shaft and disk rotate with respect to the clevis with a rate of ω disk in the direction shown below, with the angle θ increasing at a constant rate of θ. The XY Z coordinate sstem is fied with the Y -ais aligned with the fied vertical direction. The z coordinate sstem is attached to the disk with the -ais aligned with C for all time. For the position shown below, the z- and Z-aes are aligned. Find: For the position shown: (a) Determine the angular velocit of the disk. Write our answer as a vector in terms of its z components. (b) Determine the angular acceleration of the disk. Write our answer as a vector in terms of its z components. Y Z disk X C z disk 0 Use the following parameters in our analsis: θ = 0, θ = 1.5 rad/s, ω disk = 2 rad/s and ω disk = 5 rad/s 2. 3-8 Freeform c 2016
Homework 3.G Given: motor is attached to a platform that is rotating with a constant rate of ω 0 about a fied vertical ais. The bod of the motor pivots about a moving horizontal ais at a constant rate of θ with the shaft of the motor rotating at a constant rate of ω 1. Find: Determine: (a) The angular acceleration of the disk attached to the shaft of the motor. (b) The velocit of point on the disk when is at the top of the disk. Y h r disk Zz, 1 X 0 Use the following parameters in our analsis: ω 0 = 1 rad/s, θ = 30, θ = 0.3 rad/s, ω 1 = 60 rad/s, h = 0.15 m, and r = 0.1 m. Freeform c 2016 3-9
Homework 3.H Given: t the instant shown, the shaft rotates with a constant angular velocit ω 0. t the same instant, the disk spins about its ale with a constant angular velocit ω 1. Find: Determine the total angular velocit of the disk and the velocit of point C at this instant. z 750 mm 1 1 C 0 0 150 mm Use the following parameters in our analsis: ω 0 = 15 rad/s and ω 1 = 5 rad/s. 3-10 Freeform c 2016
Homework 3.I Given: rm B rotates about a fied ais with a constant rate of ω 0. disk of radius R rotates about its central ais with a constant rate of ω disk relative to the arm B. The XY Z coordinate sstem is fied with the Z-ais aligned with the fied rotation ais of B. The z coordinate sstem is attached to the disk with the -ais aligned with the upper part of the arm for all time. For the position shown below, the z aes are aligned with the XY Z aes. Find: For the position shown: (a) Determine the angular acceleration of the disk. Write our answer as a vector in terms of its z components. (b) Determine the acceleration of point on the disk. Write our answer as a vector in terms of its z components. h disk B z disk d Y 0 Z X Use the following parameters in our analsis: ω 0 = 4 rad/s, ω disk = 3 rad/s, d = 18 cm, h = 10 cm and R = 6 cm. Freeform c 2016 3-11
Homework 3.J Given: circular disk rotates about a fied vertical ais with a constant rate of Ω. strap rotates about an ais passing throughout the center of the disk with a constant rate of θ. Find: For this problem, determine: (a) The angular velocit and angular acceleration of the strap. Write our answers as vectors. (b) The acceleration of point on the end of the strap. Ω θ L Use the following parameters in our analsis: Ω = 4 rad/s, θ = 3 rad/s, θ = 36.87 and L = 300 mm. 3-12 Freeform c 2016