w = instantaneous angular speed = 1.25 rad/s
r = radius = 4.65 m
α = angular acceleration = 0.745 rad/s²
centripetal acceleration is given as
[tex] a_{c} [/tex] = rw²
[tex] a_{c} [/tex] = (4.65 ) (1.25)² = 7.27 m/s²
tangential acceleration is given as
[tex] a_{t} [/tex] = rα
[tex] a_{t} [/tex] =4.65 x 0.745 = 3.46 m/s²
angle is given as
[tex] \theta = tan^{-1}(\frac{a_{c}}{a_{t}}) [/tex]
[tex] \theta = tan^{-1}(\frac{7.27}{3.46}) [/tex]
[tex] \theta [/tex] = 64.5 deg
