Answer:
A)0.456 rev/s
B) 0.075 rev
C) 1.06 m/s
D) 3.7 m/s²
Explanation:
Initial angular velocity = [tex]\omega _{o}[/tex] = 0.270 rev/s = 1.6965 rad/s
Angular acceleration = α = 0.899 rev/s/s = 5.64858 rad/s/s
Radius = r = 0.74/2 = 0.37 m
Time = t = 0.207 s
A) Final angular velocity is given by the equation
=[tex]\omega_{f}=\omega _{o}+ \alpha t[/tex]
=1.6965 + (5.64858)(0.207) = 2.87 rad/s = 0.456 rev/s
B) No. of revolutions is calculated using the equation
[tex]\theta =\omega_{o}t + 1/2 \alpha t^2 = (1.6965 \times 0.207 )+ 1/2 (5.64858)(0.207)^2[/tex]= 0.472 rad = 0.075 revolutions
C) v = r ω =(0.37)(2.87) = 1.06 m/s
D) Centripetal acceleration = [tex]a_{c}=r\omega_{f} ^{2}[/tex] = (0.37) (2.87)² =3.05 m/s²
Tangential acceleration =[tex]a_{t}=r \alpha[/tex]
= ( 0.37)(5.64858) = 2.08997 m/s²
Resultant acceleration = [tex]a = \sqrt{a_{t}^{2} + a_{c}^{2[/tex]
= 3.697 m/s²
