00:00:30and complete it. So, we will take care of it.
00:00:34No, we will complete the vertical circular motion.
00:00:38Oh no!
00:00:42Why?
00:00:46See, here we
00:00:50start the vertical circular motion.
00:00:54So, you all know what is vertical circular motion.
00:00:58It rotates in a vertical circle.
00:01:02Let me show you.
00:01:06This is vertical circular motion.
00:01:10This is horizontal.
00:01:14This is horizontal.
00:01:18This is vertical.
00:01:22So, the body in vertical circular motion
00:01:26will rotate in a vertical circle.
00:01:30It will rotate in a vertical circle.
00:01:34Without you, no.
00:01:38Okay.
00:01:42Okay, whatever
00:01:46the formulas are, not too many.
00:01:56See, I have drawn a vertical circle.
00:02:00What have I drawn?
00:02:04Vertical circle.
00:02:08It is not visible.
00:02:12This is the bottom point.
00:02:16This is the C point and this is the D point.
00:02:20This will be the center.
00:02:24The radius of this will be r.
00:02:28Yes, all of them will be the same.
00:02:32Give me a word.
00:02:36See.
00:02:40Okay.
00:02:44See, here we have given
00:02:48velocity at the bottom.
00:02:52It will be at t is equal to zero.
00:02:56Okay.
00:03:00See, here we rotate it at theta angle.
00:03:04When it rotates at theta angle,
00:03:08its velocity will be v.
00:03:12This angle is theta.
00:03:16The mass of the particle
00:03:20will be t is equal to
00:03:24t.
00:03:28No problem.
00:03:32General time, t is equal to t.
00:03:36This t is equal to zero.
00:03:40We have given velocity v0.
00:03:44It is revolving.
00:03:48No problem.
00:03:52Now, to solve this,
00:03:56we will make a free body diagram.
00:04:00Have you heard of it?
00:04:08Circle.
00:04:12There is no oscillation.
00:04:16It is a vertical circular motion.
00:04:24We are going to make a VD of it at theta angle.
00:04:28See, from here,
00:04:32at general time,
00:04:36we have given
00:04:40velocity k.
00:04:44Here, we hold this and this.
00:04:48Then we make a VD of it.
00:04:52As soon as we reach here,
00:04:56we make a VD of it.
00:05:00Here, the force will be mg.
00:05:04This will be theta angle.
00:05:08Now, this mg will be downward.
00:05:12Here, we have connected it with a thread.
00:05:16So, tension will be towards center.
00:05:20Any problem?
00:05:24We will make it.
00:05:28We will make it here.
00:05:32See, here,
00:05:36the force is here.
00:05:40mg is downward.
00:05:44See, this angle is theta.
00:05:48Tension will be along this line.
00:05:56Yes.
00:06:00Did I make it wrong?
00:06:04See, this is the tension line.
00:06:08See, the tension along this line.
00:06:12Any problem?
00:06:16Why?
00:06:20Any problem?
00:06:24See, this is the parallel line.
00:06:28This is the vertical line.
00:06:32This is the parallel line.
00:06:36This is the similar angle.
00:06:40Any problem?
00:06:44Now, see the component of mg.
00:06:48This will be mg cos theta.
00:06:52This will be mg sin theta.
00:06:56Where is it? Oh, it was arc.
00:07:00It is not star, it is arc.
00:07:04It is moving in circular path. It should have a feeling.
00:07:08Where are you lost?
00:07:18Read it.
00:07:22We will see it later.
00:07:30See, here,
00:07:34this will be tangential acceleration.
00:07:38This will be centripetal acceleration.
00:07:42mg will be downward. This will be mg cos theta.
00:07:46Here, mg sin theta.
00:07:50Read it.
00:07:54See, mg sin theta is the only one.
00:07:58See, it is alone along this line.
00:08:02There is no force to oppose it.
00:08:06When it is not there, there will be acceleration.
00:08:10It is alone.
00:08:14If there is a force alone, there will be acceleration.
00:08:20It is in the direction of force.
00:08:24mg sin theta is here.
00:08:28In the direction of mg sin theta, there will be tangential acceleration.
00:08:32Centripetal acceleration
00:08:36will be towards the center.
00:08:40Any problem?
00:08:44No.
00:08:48Write a question.
00:08:52We will write the first question.
00:08:56t minus mg sin theta is equal to
00:09:00m into ac.
00:09:12t minus mg cos theta is equal to
00:09:16m into ac.
00:09:20Now, put the value of ac here.
00:09:24t minus mg cos theta
00:09:28is equal to mv square upon r.
00:09:32This is the first equation.
00:09:36We did not want this.
00:09:40We wanted to write v square by r.
00:09:44No problem. You can fulfill your wish.
00:09:48Do you want to fulfill your wish?
00:09:52Write it fast. We have been writing for a long time.
00:09:56You are sitting and writing.
00:10:04Where is the second?
00:10:08Write the first.
00:10:14Write the first.
00:10:18No problem.
00:10:22There is a little confusion.
00:10:26Did you write it?
00:10:34Tell me. Excuse me.
00:10:38Any problem?
00:10:44Did you write it?
00:10:48Did you write it?
00:10:56I told you.
00:11:06The second question will be from mg sin theta.
00:11:10mg sin theta
00:11:14is alone in this direction.
00:11:18Any problem?
00:11:22mg sin theta is equal to
00:11:26m into at.
00:11:30Can we cancel m from m?
00:11:34We cancelled it.
00:11:38What is the value of at?
00:11:42mg sin theta is equal to
00:11:46at.
00:11:50This is the second equation.
00:11:54We will apply kinematics in this.
00:11:58What will we apply?
00:12:02Ok.
00:12:06Be patient.
00:12:10What is the result of patience?
00:12:14At this point,
00:12:18tangential acceleration is in this direction. Velocity is in this direction.
00:12:22We take the sign convention in this direction
00:12:26as positive. Any problem?
00:12:30Do you have any problem?
00:12:34No.
00:12:38We will apply kinematics here.
00:12:46We will write the direction of velocity as positive in this direction.
00:12:50So v will be positive.
00:12:54How will be the acceleration? It will be negative.
00:12:58The value of a will be
00:13:02minus g sin theta. Any problem?
00:13:06Hello!
00:13:10Why?
00:13:14You?
00:13:18We will write at as minus g sin theta.
00:13:22We can write a as
00:13:26dv by dt.
00:13:30But we will not write directly.
00:13:34We will write at as dv by dt.
00:13:38This will be minus g sin theta.
00:13:42Any problem?
00:13:46You?
00:13:56You?
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