The disk is originally rotating at ? 0 = 8 rad/s. (Figure 1) Part A If it is sub

Question

The disk is originally rotating at ?0 = 8 rad/s.
(Figure 1)

Part A

If it is subjected to a constant angular acceleration of 7 rad/s2 , determine the magnitude of the velocity of point B just after the wheel undergoes 4 revolutions.

Express your answer to three significant figures and include the appropriate units.

Part B

Determine the magnitude of the normal component of acceleration of point B just after the wheel undergoes 4 revolutions.

Express your answer to three significant figures and include the appropriate units.

Part C

Determine the magnitude of the tangential component of acceleration of point B just after the wheel undergoes 4 revolutions.

Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

A)
wi = 8 rad/s^2
d = 4 rev = 4*2*pi rad = 25.13 rad
a = 7 rad/s^2
use:
wf^2 = wi^2 + 2*a*d
wf^2 = 8^2 + 2*7*25.13
wf = 20.4 rad/s
VB = d*wf
        = 0.45*20.4
         = 9.18 m/s
Answer: 9.18 m/s

B)
normal acceleration is same as centrepetal acceleration
aN = v^2/d
        = 9.18^2/0.45
         = 187.3 m/s^2
Answer: 187.3 m/s^2

C)
aT = d*angular acceleration
      = 0.45*7
      = 3.15 m/s
Answer: 3.15 m/s

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