Question

1/7/2019 cle travels along a portion of the "four-leaf rose" which is defined by the eqt(cos 20) along 3. A particle m. If the angular velocity of the radial coordinate line is do/dt-3t rad's, where t is in seconds, determine the radial and transverse components of the particle's velocity and acceleration at the instant 0-30o. At t-0, 0-0 CHECK: v--16.9 m/s, ar 89.4 m/s, 5 cos 29

Answer 1

Step 1 Given at t = 0, theta = 0 degree find t = ? theta = 30 degree use relation d theta/dt = theta dot = 3t^2 rad/s integrate both sides integral d theta = integral 3t^2 dt theta = (3t^3/3) + c c = 0 as given (theta = 0 @ t = 0) theta = t^3 t = theta^1/3 = (pi/6)^1/3 step 2 V_radius = r dot = d/dt (5 cos 2 theta) = 5(-sin 2 theta) middot 2 middot d theta/dt put theta = 30 degree and d theta/dt = 3t^2 = -5 sin 60 degree times 2 times 3t^2 Now, put t = (pi/6)^1/3 = -5 times sin 60 degree times 2 times 3 times (pi/6)^2/2 = -16.88 m/s \r\n step 3 a_t = r theta dot = (5 cos 2 theta) middot d theta/dt = 5 cos 2 theta times 3t^2 = 5 times cos 60 degree times 3 times (pi/6)^2/3 = 4.87 m/s Step 4