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rock.freak667

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You'd only get a tangential acceleration if the pendulum's velocity changes with time.

[tex]a_t=\frac{dv}{dt}[/tex]

If the angular velocity is constant, then so is the velocity and hence there will be no tangential acceleration.

EDIT: read dx's post...I thought of the pendulum situation incorrectly. Sorry.

[tex]a_t=\frac{dv}{dt}[/tex]

If the angular velocity is constant, then so is the velocity and hence there will be no tangential acceleration.

EDIT: read dx's post...I thought of the pendulum situation incorrectly. Sorry.

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How is the angular velocity constant?

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dx

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I don't understand that because I have not learned about force or tension yet.

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rock.freak667

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From http://en.wikipedia.org/wiki/Tension_(mechanics)" [Broken]]:I don't understand that because I have not learned about force or tension yet.

tension is the magnitude of the pulling force exerted by a string, cable, chain, or similar object on another object. It is the opposite of compression

Basically if you put a weight on a string, which will cause it to extend, the tension is a force which resists this extension.

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@einstein- I just made that problem up, so you guys could help me.

Is there a way to show this with just kinematics and not dynamics? In the book this chapter is before the dynamics part and I think they expect me to know why with what we have learned.

Sorry for being a not being understanding.

Is there a way to show this with just kinematics and not dynamics? In the book this chapter is before the dynamics part and I think they expect me to know why with what we have learned.

Sorry for being a not being understanding.

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At all times, there are only 2 forces on the pendulum, that of gravity, and that of the tension from the pendulum arm. The tension from the pendulum arm is always directed towards the center of the arc traced by the pendulum. This tension results in centripetal (center-seeking) acceleration. You know when you're riding shotgun in a car and the driver makes a hard left turn, and you feel the pressure of the car door or armrest on your right side? This is a result of the car accelerating towards the center of the arc-turn it is making (this is best conceptualized from a top-down view). This is another form of centripetal acceleration. Centripetal acceleration is always directed towards the center, so by itself it cannot result in tangential acceleration (which, by definition, is acceleration from a force that is tangential to the circle).

The other force involved, gravity, is of course always pointed directly down. Imagine the pendulum at 90 degrees from the vertical position, i.e. it is sticking directly out to the left or right. At this point the gravity force is completely tangent to the instantaneous velocity of the pendulum (which would also be pointed directly down here. In fact, this is a good way to explain tangential acceleration, it must be parallel to the direction of the instantaneous velocity.) As the pendulum falls, its instantaneous velocity changes, from pointing directly down when it first starts falling, to being horizontal at the bottom of the arc. Before it hits the bottom, while its still falling, the combined forces of gravity and tension result in a tangential acceleration (this is the hardest part to visualize, best done by drawing the vectors forces from each and combining them together).

However, at the bottom the force of gravity is completely perpendicular to the motion of the pendulum. Gravity doesn't contribute to purely horizontal motion, so no tangential acceleration either. This is basically what dx said, but it seemed like you needed more of a background, so I went off into a rant.

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dx

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dx

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dx

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Didn't I explain that already in post #4? What didn't you understand in that?

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I don't know anything about dynamics yet, so I didn't understand.

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ideasrule

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Gravity always pulls down; that's pretty obvious. When a string is stretched, it pulls back along its length. In a pendulum, that would be towards the pivot.

At the bottom of the pendulum's arc, gravity pulls the bob down while tension pulls it up. There's nothing pulling sideways--"tangentially", as you called it--so there's no reason for the bob to change its speed. That's why tangential acceleration is zero.

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