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a fan rotating with 100 rad/sec is swtched off .after 2n rotation its aangular velocity become 50 rad/sec.find angular velocity of fan after n rotation

a fan rotating with 100 rad/sec is swtched off .after 2n rotation its aangular velocity become 50 rad/sec.find angular velocity of fan after n rotation

Grade:11

1 Answers

Khimraj
3007 Points
2 years ago
Angular displacement in 2n rotations is4n\pi.Hence from equation of motion,\omega^2-\omega_0^2=2\theta \alpha\implies \alpha=\dfrac{50^2-100^2}{2(2n\pi)}=-\dfrac{7500}{8n\pi}Hence angular velocity after n rotations=\sqrt{\omega_0^2+2\alpha\theta_2}=\sqrt{100^2-2\dfrac{7500}{8n\pi}(2n\pi)}=79rad/sec

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