Answer
Given,
Revolution of wheel = 23 rev.
= 23 x 2π = 46 π
Time = 3 s
final angular velocity = 16 rad/s
angular acceleration of wheel = ?
Now, Calculating the initial angular speed of the wheel
Angular displacement = [tex]\dfrac{1}{2}[/tex](initial velocity + final velocity) x time.
[tex]46 π = \dfrac{\omega_o+16}{2}\times 3[/tex]
[tex]\omega_0 = 80.29\ rad/s[/tex]
now, angular acceleration
[tex]\alpha = \dfrac{\omega-\omega_0}{t}[/tex]
[tex]\alpha = \dfrac{16-80.29}{3}[/tex]
[tex]\alpha = -21.43\ rad/s^2[/tex]
Hence, the angular acceleration of wheel is negative means wheel is decelerating.
The angular acceleration of the wheel is negative (-).
The angular acceleration would be the temporal ratio during which the angular speed changes and therefore is commonly denoted by alpha (α) as well as written throughout radians/sec.
According to the question,
Revolutions, 23 rev or,
23 × 2π = 46π
Time, 3 seconds
Final angular velocity, 16 rad/s
We know the formula,
→ Angular displacement = [tex]\frac{1}{2}[/tex] (Initial velocity + Final velocity) × Time
By substituting the values,
46 = [tex]\frac{\omega_o +16}{2}[/tex] × 3
[tex]\omega_o[/tex] = 80.29 rad/s
hence,
The angular acceleration will be:
→ α = [tex]\frac{\omega - \omega_o}{T}[/tex]
= [tex]\frac{16-80.29}{3}[/tex]
= -21.43 rad/s²
Thus the above response is correct.
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