Question

The fan blades suddenly experience an angular acceleration of 2 rad/s2. If the blades are rotating with an initial angular velocity of 4 rad/s, determine the magnitude of the acceleration of point P when the blades have turned 2 revolutions. Ch16Prob4

a.115.95 ft/s^2
b.116 ft/s^2
c.0ft/s^2
d.3.5 ft/s^2

Answer 1

Option B

`116 ft/s^(2)`

Step-by-step explanation:

`\theta=2 rev=2(2\pi)=4\pi`

`\alpha \theta=0.5(\omega_f^(2)-\omega_i^(2))`

`\alpha (4\pi)= 0.5(\omega_f^(2)-\omega_i^(2))`

`\alpha (8\pi)= (\omega_f^(2)-\omega_i^(2))`

`(2) (8\pi)= (\omega_f^(2)-\omega_i^(2))`

`(2) (8\pi)= (\omega_f^(2)-4^(2))`

`\omega_f=8.14 rads/s`

`v=r\omega=1.75*8.14=14.245 ft/s`

Centripetal acceleration
`=\omega_f^(2) r=8.14^(2)*1.75=115.95 ft/s^(2)`

Tangential component=dr=2*1.75=3.5

`Resultant=\sqrt{3.5^(2)+115.95^(2)}\approx 116 ft/s^(2)`