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# Race cars with constant speed around curve

When acceleration could involve a change in direction and not speed. Created by Sal Khan.

## Want to join the conversation?

• I dont understand how change of direction can effect acceleration? Formula a=v/t does not indicate that? •   night3x: You are right in the last statement. Direction has nothing to do with speed.
Speed and Velocity are not the same thing, so direction is an integral part of velocity, it is needed to describe velocity, whereas speed is defined only by a quantity, a number if you will, saying how fast something goes - but not to where.

Velocity on the other hand, has to say how fast and which way.
This is why you can only have speed which is a positive number (or zero), but velocity can be a negative number as well (moving at some speed in an opposite direction).

I hope I did not introduce more confusion in all this :)
• Is the concept similar, when the second hand on a clock makes one complete revolution in 1 minute? is the tip of the second hand accelerating? • Would the driver be depressing the gas pedal to accelerate and therefore maintain his speed through the turn even though the speedometer still reads 100 mph? • No. Two different accelerations in that case. The centripetal (center seeking) acceleration is what you feel when you round a curve and you're thrown outward. It is always inward or perpendicular to the curve.

If the drivers speed is constant then there is no acceleration that is tangential to the curve. You'd experience this acceleration, if there was one, by being pushed back into the seat.

The most likely reason the driver would need to depress the gas pedal is that there is some loss due to the friction between the tires and the road and/or the air resistance of the car.

Goes back to Newton's first law if there were no external forces acting on that race car it would speed along happily at 100 mph forever without any need for added force.
• could this also be represented as a planetary system where the cars are planets, the center of the track is the sun, and the acceleration towards the center is gravity? If this could be represented this way it would be a lot easier for me to understand. • suraj1997pisces is on the right track. Gravity does half the work of keeping the planets in orbits, accelerating toward the sun. The other half of the equation, so to speak, is the angular momentum caused by the planet racing around the orbit. This momentum is best demonstrated by swinging a ball on a string around your head. So long as you hold onto the rope (gravity) the ball stays in its orbit, though it tugs outward on the string (angular momentum). If you let go of the string, the ball flies away from you in a straight line. This line is a tangent to the orbit, which is always a circle or ellipse.

So long as the two forces (gravity and angular momentum) are stable, the orbit is stable. The car or planet or ball goes around and around forever. But once one force or the other gets out of balance, the orbit decays. If gravity > angular momentum, the object accelerates toward the center of the star or whatever. If gravity < angular momentum, the object accelerates away from the center.
• If centrifugal force is a "fictitious" force, how are we able to feel it? • If you start moving on a straight line (say with constant velocity), by the inertial principle, you'll tend to continue with that movement!

When, in a car, you take the curve the velocity changes... but your body still wants to move in a straight line. Respect to the car, your body goes in the oposite direction than the curve... So it is interpreted as if a "force" is pushing you outside the car. (This is what we know as centrifugal force)

Nonetheless, the real thing is that the sit, sitbell, the door, and any part of the car you are sticked to, are pulling you inside the car! (This is the real deal... the centripetal force)

Cheers!
• Why is the acceleration vector towards the center of the circle if we feel a push towards the outside of the circle? • I have a quick question what would happen if it was an oval would it accelerate? • Good question!

Lets put it this way, oval has changing radius and velocity vector (direction). The side of the oval has longer radius and the top and the bottom of the oval has less radius; the oval has two sharp turns and two smooth turns each 2(pi) radian (360, full circle). Centripetal force does not have to change since velocity can accelerate to a certain velocity that is compatible to the radius of the oval. But if it changes, it must be in a certain Newtons depending on the radius of the oval. The car therefore accelerate and does not accelerate due to the fact that the Centripetal force changes. And to prove it, here is an example:

F(centripetal)=m(mass will stay the same since mass cannot be neither created nor destroyed)v^2 divided by r (radius)

I have told you that the radius constantly changes so I will plug in two random radius.

1000 N (we're keeping the force same)=100kg(weight of a car)x 20m/s(speed)^2 divided by 40 meters

and

1000N =100kg(v^2) divided by 20 meters

With some algebra, we get:
20000kg(m^2)/s^2=100kg(v^2)
200m^2/s^2 =v^2(m/s)
approx(14.14m/s) =v

And if the Centripetal force changes, speed remains the same.
Check this one out:

1000N =100kg(20m/s^2) divided by 40

2000N =100kg(20m/s^2) divided by 20

Now these works are just one of a gazillion part of the motion I showed you. The reason why I say gazillion is because the radius constantly changes. If the object were to accelerate, velocity would constantly change every Planck time (smallest possible time). And if the Centripetal force were to change, it would constantly change to maintain the velocity of the car.

Hope it helped!
• does it mean that planets orbiting the sun are constantly accerating  • 