Consider two pendula consisting of a piece of clay stuck to a massless rigid rod
ID: 1775437 • Letter: C
Question
Consider two pendula consisting of a piece of clay stuck to a massless rigid rod, which is pivoted at its end. The two | CEILING pendula are released from a horizontal orientation, as pivot . drawn here, and allowed to swing down. On pendulum 1, the clay is stuck to the midpoint of the rod. On pendulum 2, it's stuck to the end of the rod. In both cases, the rods have the same length, and the pieces of clay have the same mass. And in both cases, the pendulum swings down because a torque due to gravity acts an the clay. (Remember, the rod is essentially massless.) 11. pivo Pendulum 1 Pendulum 2 (a) What's different about pendulum 1 vs. pendulum 2: The rotational inertia, the torque, or both?Explanation / Answer
1) both are different .
Rotational inertia = mR^2
Torque = F×R
As R is different for both, both quantities will vary.
2) See formula for torque, tau2 has 2 times radius than case 1.
So tau2 is twice times as tau1.
3) Inertia has R^2 term. So I2 will 4 times as I1.
4) the rod which will have high angular acceleration will reach bottom faster.
Write torque equation about pivot point.
Tau = I . a
Tau is torque ,I is rotational inertia and a is angular acceleration.
For case 1 , we get a1 =2g/R
And for case 2
a2 = g/R
So pendulum 1 will reach bottom earlier.