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a disk of radius 10 cm speeds up from rest. it turns 60 radians reaching an angular velocity of 15 rad/s. what was the angular acceleration?
b. how long did it take the disk to reach this velocity?​

Sagot :

Answer: [tex]1.875\ rad/s^2, 8\ s[/tex]

Explanation:

Given

Radius of disc [tex]r=10\ cm[/tex]

Angle turned [tex]\theta=60\ rad[/tex]

Initial angular velocity [tex]\omega_0=0[/tex]

Final angular velocity [tex]\omega_f=15\ rad/s[/tex]

using [tex]\omega^2-\omega_o^2=2\alpha \cdot \theta[/tex]

Substitute values

[tex]\Rightarrow 15^2-0=2\times \alpha \times 60\\\Rightarrow \alpha=1.875\ rad/s^2[/tex]

using [tex]\omega=\omega_o+\alpha t[/tex]

Substitute values

[tex]\Rightarrow 15=0+1.875\times t\\\Rightarrow t=8\ s[/tex]

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