2.62. A particle of mass m slides on a smooth rod of length...

2.62. A particle of mass $m$ slides on a smooth rod of length $l$ and mass $m$ that is pivoted in a vertical plane (Fig. P2.62). (a) Derive the equations of motion. (b) Assuming that the system is initially at rest, with $\theta(0) = 0$ and $r(0) = l/2$, determine the initial reaction at the pin.

Transcript

00:01 So we have a diagram here with a fulcrum and, whoops, two masses.

00:22 L1 is here, l2 is here.

00:26 Okay.

00:29 So we're told that l1 is 20 centimeters, and l2 is 80 centimeters.

00:49 Okay.

00:50 With the magnitude of the accelerations on particles 1 and 2.

01:15 Okay.

01:17 So, the inertia of this system would be the sum of the masses times the distance is squared.

01:32 I don't think we're told numbers for the mass, but they're the same.

01:39 So the inertia would be, and i'm making this the positive direction, anyway, it would be, well, total inertia, it doesn't matter on the direction.

01:56 It's just going to be the sum of the mr squares, which would be mass times l1 squared plus mass times l2 squared.

02:07 But i'm just going to change that to factor out the m.

02:14 Okay.

02:15 Now, the torque net, this is where i need the direction, is going to be m times g at l1.

02:35 So m -g -l -1 minus m -g -l -2.

02:45 That's going to be i alpha we're trying to figure out alpha so alpha is going to be factoring out the m g who m g it's not a not a subscript l1 minus l2 over i but i is m l1 squared plus l2 squared oops, i erase a draw.

03:27 Okay.

03:29 So, then the acceleration at 1 is going to be alpha times the distance to 1, which would be l1.

03:41 The acceleration at 2 is going to be alpha times the distance to 1, to l2.

03:53 So putting this all together in a calculator, i'm going to write, first of all, i'm going to declare l1 and l2.

04:05 And i finally figured out, if you just type l1, it puts in a subscript automatically.

04:10 E equals 0 .02...

Question

2.62. A particle of mass $m$ slides on a smooth rod of length $l$ and mass $m$ that is pivoted in a vertical plane (Fig. P2.62). (a) Derive the equations of motion. (b) Assuming that the system is initially at rest, with $\theta(0) = 0$ and $r(0) = l/2$, determine the initial reaction at the pin.

Please give Ace some feedback