Explanation:
Given that,
Diameter of the wheel, d = 70 cm = 0.7 m
Initial angular speed, [tex]\omega_i=160\ rpm=16.75\ rad/s[/tex]
Final angular speed, [tex]\omega_f=280\ rpm=29.32\ rad/s[/tex]
Time, t = 4 s
(a) Angular acceleration,
[tex]\alpha =\dfrac{\omega_f-\omega_i}{t}\\\\\alpha =\dfrac{29.32-16.75}{4}\\\\\alpha =3.14\ rad/s^2[/tex]
(b) Tangential acceleration is :
[tex]a=r\alpha \\\\a=0.35\times 3.14\\\\a=1.085\ m/s^2[/tex]
Angular speed of the wheel after 2 seconds is :
[tex]\omega_f=\omega_i+\alpha t\\\\\omega_f=16.75+3.14\times 2\\\\\omega_f=23.03\ rad/s[/tex]
Radial acceleration will be :
[tex]a=\omega_f^2r\\\\a=(23.03)^2\times 0.35\\\\a=185.6\ m/s^2[/tex]
Hence, this is the required solution.
