Question

A 70-cm-diameter wheel accelerates uniformly from 160rpm to 280rpm in 4.0s. Determine (a) its angular acceleration, and (b) the radial and tangential components of the linear acceleration of the point on the edge of the wheel 2.0s after it has started accelerating?

Answer 1

Explanation:

Given that,

Diameter of the wheel, d = 70 cm = 0.7 m

Initial angular speed, $\omega_i=160\ rpm=16.75\ rad/s$

Final angular speed, $\omega_f=280\ rpm=29.32\ rad/s$

Time, t = 4 s

(a) Angular acceleration,

$\alpha =\dfrac{\omega_f-\omega_i}{t}\\\\\alpha =\dfrac{29.32-16.75}{4}\\\\\alpha =3.14\ rad/s^2$

(b) Tangential acceleration is :

$a=r\alpha \\\\a=0.35\times 3.14\\\\a=1.085\ m/s^2$  

Angular speed of the wheel after 2 seconds is :

$\omega_f=\omega_i+\alpha t\\\\\omega_f=16.75+3.14\times 2\\\\\omega_f=23.03\ rad/s$

Radial acceleration will be :

$a=\omega_f^2r\\\\a=(23.03)^2\times 0.35\\\\a=185.6\ m/s^2$

Hence, this is the required solution.