Question

a uniform rod of length l hinged at one end is free to rotate in the vertical plane if the rod is held jorizontal at the begining and released then thr angular velocity of the rod when it makes an angle of 60° with the vertical for the first time is ​

Answer 1

The angular velocity of the rod when it makes an angle of 60° is ω^2  = √ 3g/2l.

Explanation:

As we know that:

1/2 ML^2/3 ω^2 = Mg L/2 sin (30°)

ω^2  = 3gL / L^2 sin(30°)

ω^2  = 3g /l x 1/2

ω^2  = √ 3g/2l

Thus the angular velocity of the rod when it makes an angle of 60° is ω^2  = √ 3g/2l.

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A man of mass 70 kg stands on a weighing scale in a lift which is moving (a)upwards with a uniform speed of 10 metre per second (b)downwards with the uniform acceleration of 5 metre per second square case ? what would be the reading if the lift mechanism failed and it hurtled down freely under Gravity?​

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