Rotational MotionHard
Question
A circular plateform is free to rotates in a horizontal plane about a vertical axis passing through its centre. A tortoise is sitting at the edge of the plateform. Now the plateform is given an angular velocty ω0. When the tortoise move along a chord of the plateform with a constant velocity (with respect to the plateform). The angular velocity of the platefor ω(t) will vary with time t as
Options
A.
B.
C.
D.
Solution
Since, there is no external torque, angular momentum will remail conserved. The moment of inertia will first decrease till the tortoise moves A to C and then increase as it moves from C and D. Therefore, ω will be initially increases and then decreases.
Let R be the radius of plateform, m the mass of the disc and M is the mass of plateform
Moment of inertia when the tortoise is at A
I1 = mR2 +
and moment of inertia when the tortoise is at B
I2 = mr2 +
Here, r2a2 +
From conservation of angular momentum
ω0I1 = ω(t)I2
Substituting the values wecan see taht variation of ω(t) is non-linear.
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