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So let us look at an example where we apply Newton's second law by using cylindrical coordinates.

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Now, what I've illustrated in a figure here is a tennis ball with a weight of zero point zero five

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six kg, which is swung around a ball.

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The string to which the tennis ball is attached slides down the pole.

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Such that its position in the Z direction is given by miners to T meters, so you can see it's negative

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because we measure the zero position at the top and it slides down.

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At the same time, the length of the string is increased according to or is equal to zero point one

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to meters, while the angular velocity is given by Theta Dot, which is seven radians per second.

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So you can see in the question I give you theatergoer directly.

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I do not say theta is equal to seven D, I say theta that is seven.

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I give you the angular acceleration immediately.

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So the question is determine the forces experienced by the ball in the theater direction, the radial

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direction and the direction at the instance at the instant when D three seconds.

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So let us have a look.

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We have formulas for the acceleration in each one of these directions.

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OK, we know that the acceleration of the radial direction is all double minus or theatergoer squared

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and that the acceleration in the theater direction is or doubled that plus two or three to dot, and

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that the acceleration in the Z direction is a double dot.

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And we have been given.

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Functions of time for each one of these coordinates.

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We've been told that the position in the Z direction is given by minus two to that, that our position

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is given by zero comma one T and that theta dot, that angular velocity is given by seven radians per

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second.

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So let's apply that in our formulas.

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The sum of the forces in the right direction is the mass multiplied by the acceleration in the right

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direction.

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That is the mass multiplied by our double dot minus or theta that squared, which is the mass multiplied

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by now.

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We have been given all.

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And if we take the second derivative of or we find that it is zero minus or is zero point one dy multiplied

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by theta that square we've been given theatergoer seven.

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And if we plug in to be three seconds, we get a force of minus zero eight two, three, two Newtons.

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Now we have implicitly assumed.

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That the outward direction is positive.

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Because I've said in the question that the length of the string is increased according to or is equal

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to zero comma one T. So an increase in length is positive.

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Right.

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And so positive is outward.

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And therefore, because we get a negative answer for the fourth, it means the forces in the direction

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of the poll, the force is inward, which makes sense because that is what keeps the the ball from from

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flinging out.

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Then we look at the some of the forces in the theater direction, that's mass multiplied by the acceleration

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of the theater direction, that's m multiplied by our theater.

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Double plus two are not theater that that is M multiplied by or a zero one T theater double that.

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We've been given theater dot as seven radiance per second.

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That's a constant.

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So Tom derivative of DataDot will be zero plus two.

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Tom, derivative of all that zero point one multiplied by we've been given theatergoer as seven, and

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if you substitute in 340 you get zero zero seven eight for Newton in the theater direction.

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Now, the sum of the forces in this direction is multiplied by A-Z, and we know that the acceleration

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of the direction, that's the second derivative of the Z position.

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We have been told in the question that the ball slides down the pole according to minus zero to T..

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So the first derivative of that.

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Would be minus zero two and the second derivative would be zero.

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So we see that there is no force in the Z direction.

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Now, be careful how you interpret this, the ball slides down so clearly something is working in on

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the ball, but there is no acceleration in this direction.

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The sum of the forces in this direction is zero because, of course, we have the force of gravity working

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down, but the friction.

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Where the rope is attached to the pole is working up and therefore we only have a constant velocity

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going in the same direction, meaning the acceleration in the same direction is zero.

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And if the acceleration in a certain direction is zero, then we know the sum of the forces in that

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direction is zero.

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So there is no need to force acting on the ball in the direction that is what this result implies,

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and if you read the question, you could see that because it said that such that its position in the

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Z direction is given by minus zero comma to T. So it means that the position is a linear function of

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T, that means the velocity will be constant.

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That means the acceleration will be zero in the direction, meaning there is also no net force in this

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direction.

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So that is why this result of zero neutral force in the Z direction.

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Makes sense, and if I say zero and force, I mean resultant force, the sum of the forces in this direction

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is zero.

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So this.

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Example plus, the previous video serves to show you the basic principles of Newton's second law in

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cylindrical code, and it's now not that no matter in which coordinate system we apply Newton's second

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law, it does not change the law.

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It's just that if we applied in a different coordinate system, we use different parameters to describe

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the position of the particle and therefore we also use different parameters to describe the velocity

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and then the acceleration of the particle.

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That is why the formulas for acceleration look different in each one of the coordinate systems.

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If we use rectangle coordinates, we would have.

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Found that the same forces work in on the status for.

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But it would have just been a long, different coordinate axis, because that is how we would have set

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up the coordinate system.

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So I just want to stress that Newton's second law remains universal in this case, and it's just the

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coordinate systems that change.