ME 251 DynamicsIssued 2015 Nov. 4th Handout #HW 8 Due by 2015 Nov. 11th Honor Code: I have neither given nor received the details of the problems from anyone and/or any existing solutions prepared by others when completing the final written work. Name: Signature: ※ Estimate hours you spent to complete this homework including course review: hrs. (숙제의 난이도 조절을 위해 학생들의 숙제 풀이 소요시간을 모니터 하고자 하니 대략적으로 숙제 및 숙제를 위한 공부시간을 기재하시오) ※ Homework without written honor code & signature won’t be accepted (숙제 맨 앞장에 위에 기재된 명예규정을 친필로 쓰고 싸인 하지 않은 숙제는 채점하지 않음). ※ Violation of the honor code for completing HW will give both the copy and the original ZERO credit and ONE LETTER GRADE DISCOUNT (1st violation) or F CREDIT (2nd violation). 1. (20 pts) Suppose a circular disk is rolling on the surface without slipping. In the given figure, the coordinate frame A whose basis vectors are 𝐞̂𝐴1 and 𝐞̂𝐴2 is a global frame (which is neither moving nor rotating), and the coordinate frame B whose basis vectors are 𝐞̂𝐵1 and 𝐞̂𝐵2 is a body-fixed frame moving and rotating with the disk. Here, 𝑥(𝑡) is the distance and 𝜃(𝑡) is the angle between the A and B coordinate frames at time t, and the disk is rotating at a constant speed of 𝜔 = 𝜃̇. P is the intersection point between on the axis of 𝐞̂𝐵1 and the edge of the disk. (a) Find 𝐫𝑃 (𝑡), which is the position vector from A to P , in the A coordinate frame. (b) Find the velocity vector 𝐯𝑃 (𝑡) in the A coordinate frame. (c) Find the acceleration vector 𝐚𝑃 (𝑡) in the A coordinate frame. (d) Evaluate 𝐯𝑃 and 𝐚𝑃 when 𝜃 is 0 o, 90 o and 180o. ME 251 Dynamics Issued 2015 Nov. 4th Handout #HW 8 Due by 2015 Nov. 11th 2. (20 pts) Determine the angular velocity of link AB and the velocity of collar B for the instant depicted. Assume the quantities 𝜔0 and r to be known. 3. (20 pts) The large roller bearing rolls to the left on its outer race with a velocity of its center O of 1 m/s. At the same time the central shaft and inner race rotate counterclockwise with an angular speed of 300 rev/min. Determine the angular velocity 𝜔 of each of the rollers. ME 251 Dynamics Issued 2015 Nov. 4th Handout #HW 8 Due by 2015 Nov. 11th 4. (20 pts) An experimental vehicle A travels with constant speed 𝑣 relative to the earth along a north-south track. Determine the Coriolis acceleration 𝐚Cor as a function of the latitude 𝜃. Assume an earth-fixed rotating frame Bxyz and a spherical earth. If the vehicle speed is 𝑣 = 300 km/h , determine the magnitude of the Coriolis acceleration at (a) the equator and (b) 45o latitude (c) the north pole. 5. (20 pts) Under the action of its stern and starboard bow thrusters, the cruise ship has the velocity 𝑣𝐵 = 2 m/s of its mass center 𝐵 and angular velocity 𝜔 = 1.5 deg/s about a vertical axis. The velocity of 𝐵 is constant, but the angular rate 𝜔 is decreasing at 0.5 deg/s2. Person 𝐴 is stationary on the dock. What velocity and acceleration of 𝐴 are observed by a passenger fixed to and rotating with the ship? Treat the problem as two-dimensional.