Question

The angular position of a rod varies as 21.712 radians from time . The rod has two beads on it as shown in the following figure, one at 11 on from the rotation axis and the other at r = 34 cm from the rotation axis. (Note: figure may not be drawn to scale.) Counterclockwise rotation Axis of rotation 1 (a) What is the instantaneous angular velocity (in rad/s) of the rod at - (Indicate the direction with the sign of your answer. Round your answer to at least one decimal place.) O rad/s (b) What is the angular acceleration (in rad/s) of the rod at - 987 (Indicate the direction with the sign of your answer.) rad/s2 ( What are the tangential speeds of the beads (in m/s) at: (6) What are the tangential accelerations of the beads at 9 (Enter the magnitudes in m/s2.) (w) What are the centripetal accelerations of the beads at 92 (Enter the magnitudes in m/s2.) - Additional Materials Book

Answer 1

given that

$\Theta$ = angular position = 21.7 t^2 rad

a) angular speed w = d$\Theta$/dt = 2*21.7t = 43.4 t rad/s

at t = 9 sec

w = 173.6 rad/s

b) angular acceleration = dw/dt = 43.4 rad/s^2

c) tangential speed v = rw

at t = 9 sec

vt,1 = 0.13*43.4*9 = 50.8 m/s

vt,2 = 0.34*43.4*9 = 59.02 m/s

d) tangential acceleration

at = r*alpha

at,1 = 0.13*43.4 = 5.64 m/s^2

at,2 = 0.34*43.4 = 14.76 m/s^2

e) centripetal acceleration ac = v^2/r

ac,1 = 50.8^2/0.13 = 19851.1 m/s^2

ac,1 = 59.02^2/0.34 = 10245.2 m/s^2