Question

with radius To rotates at a constant angular velocity θ(t) in the counterclockwise direction. At time t - 0, a small spherical ball, which is modeled as a particle, is rolled without slipping at a constant speed vo from the edge at A toward the origin of the rotating disk. Formulate the equations of motion and solve them. Plot the trajectory of the ball from both the moving and inertial frame. You can use MATLAB to solve the equations and to obtain the plots 0 ou) 3. An excavator is shown in the figure shown below. Link OA has length 2.5m and link AB has length I 18m. The bucket is attached at joint B. At the instant shown, e 70°,6 0.1 ,#2-001 rad-P 50°,ф--0.5 rad , ф :0 Compute acceleration of the bucket with respect to the fixed coordinate frame e the absolte velocity and Homework 2 ced 2019

Please solve question 3, thanks

Answer 1

Given that radius of disk r_0 angular velocity constant theta(epsilon) at t = 0, ball is rolled without at constant speed v_0 from A toward origin alpha-qudin of motion in rotating frame can be written as mw bar = F + mw^2 R 2mv times w = F bar + F bar m F bar m being resultant initial force at A -2mw^2 1^2 n + 2mv� wn = 0 -2m (theta(eta))^2 r_0 n + 2mv� wn = 0 -2m (theta(eta))^2 r_0 n + 2mv(theta� (epsilon)n = c \r\n thus, v� = w^2 w = v1^2/c = v^2/n = w^2/0 Fm = mw^2 alpha rightarrow + mw^2 b c rightarrow mw^2 squareroot 4r_0^2 - r^2 = Vertical-bar F bar m Vertical-bar Fm = m(v_c(-)^2 squareroot 4^2 0^2 - r62 theta = wt total distance a point on origin that rm cases s(t) = r_0 theta(t) radial and tangential components = r_0 w a radial = w^2 r therefore we have radius r_0 as constant so we have