Question

The disk of radius 0.4 m is originally rotating at ωo=4 rad/sec. If it is subjected to a constant angular acceleration of α=5 rad/sec, what is the magnitudes of the normal component of acceleration of a point on the outer surface of the disk (0.4 m from the center) at the instant t=1 sec. a. 32. 4 m/sec^2 b. 81.8m/sec^2 c. 60.33 m/sec2 d. 4.33 m/sec2

Answer 1

Answer:32.4m/$s^2$

Explanation:

Given data

$radius\left ( r\right )$=0.4m

Intial angular velocity$\left ( \omega_0\right )$=4rad/s

angular acceleration$\left ( \alpha\right )$=5rad/$s^2$

angular velocity after 1 sec

$\omega$=$\omega_0$+$\alpha\times\t$

$\omega$=4+5$\left ( 1\right )$

$\omega$=9rad/s

Velocity of point on the outer surface of disc$\left ( v\right )$=$\omega_0\timesr$

v=$9\times0.4$ m/s=3.6m/s

Normal component of acceleration$\left ( a_c\right )$=$\frac{v^2}{r}$

$a_c$=$\frac{3.6\times3.6}{0.4}$=32.4m/$s^2$