- Tardigrade
- Question
- Physics
- A circular platform is free to rotate in a horizontal plane about a vertical axis passing through its centre. A tortoise is sitting at the edge of the platform. Now the platform is given an angular velocity ω0 When the tortoise move along a chord of the platform with a constant velocity (with respect to the platform). The angular velocity of the platform ω (t) will vary with time t as
Q. A circular platform is free to rotate in a horizontal plane about a vertical axis passing through its centre. A tortoise is sitting at the edge of the platform. Now the platform is given an angular velocity When the tortoise move along a chord of the platform with a constant velocity (with respect to the platform). The angular velocity of the platform will vary with time t as
Solution:
Since, there is no external torque, angular momentum will remain conserved. The moment o f inertia will first decrease till the tortoise moves from A to C and then increase as it moves from C and D. Therefore, (0 w ill initially increase and then decrease.
Let R be the radius o f platform, m the mass o f disc and M is the mass o f platform.
Moment o f inertia when the tortoise is at A
and moment o f inertia when the tortoise is at B
Here ,
From conservation o f angular momentum
Substituting the values we can see that variation o f is non-linear.
