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A turntable rotates with a constant 1.85 rad/s2 clockwise angular acceleration. After 4.00 s it has rotated through a clockwise angle of 30.0 rad . Part A What was the angular velocity of the wheel at the beginning of the 4.00 s interval?

Answer :

Answer: The angular velocity of the wheel at the beginning of the 4.00 s interval is 3.8 rad/s

Explanation: Please see the attachment below

${teks-lihat-gambar} Abdulazeez10
onyebuchinnaji

The angular velocity of the wheel at the beginning of the 4.0 s time is 3.8 rad/s.

The given parameters:

  • Angular speed of the turn table = 1.85 rad/s²
  • Time of motion, t = 4.0 s
  • Angular displacement, θ = 30.0 rad

The angular velocity of the wheel at the beginning of the 4.0 s time is calculated as follows;

[tex]\theta = \omega_i t + \frac{1}{2} \alpha t^2[/tex]

where;

[tex]\omega_i[/tex] is the initial angular velocity

[tex]30 = \omega_i (4) \ + \frac{1}{2}(1.85)(4)^2\\\\30 = 4\omega _i + 14.8\\\\4\omega _i = 30 - 14.8\\\\ 4\omega _i = 15.2\\\\\omega _i = \frac{15.2}{4} \\\\\omega _i = 3.8 \ rad/s[/tex]

Thus, the angular velocity of the wheel at the beginning of the 4.0 s time is 3.8 rad/s.

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