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`

Step-by-step 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*\t`

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

`\omega`=9rad/s

Velocity of point on the outer surface of disc
`\left ( v\right )`=
`\omega_0*r`

v=
`9*0.4` m/s=3.6m/s

Normal component of acceleration
`\left ( a_c\right )`=
`(v^2)/(r)`

`a_c`=
`(3.6*3.6)/(0.4)`=32.4m/
`s^2`