Which Way Will the Wheel Spin? You May Be Surprised

aka Under the ruler faster than the ruler
Xaxsays...

I'm curious to know why the big wheel moves in the opposite direction of the ruler. My best guess is that it has to do with the small amount of surface contact, but I don't know for sure. I think I understand why the cart moves faster than the ruler, although it's hard for me to put into words, and I'll probably look really dumb if I try.

rottenseedsays...

Easy stuff. The ruler pushes on the big wheel. The contact between the 2 produces static friction. According to Newton's 3rd law, every action there is an equal but opposite reaction so you end up with this chain reaction.

ruler pushes on big wheel to the right-->big wheel pushes back to the left-->contact with little wheels then causes them to go to the right-->wheels push on ground-->ground pushes back...cart goes right.

The reason it goes faster than the ruler is because of mechanical advantage. (Distance from effert exerted)/(Distance resulting from effort)

Throbbinsays...

It comes down to leverage. Notice how he tips the ruler while pushing it. This gets the round thing going in a certain way, and inertia keeps it rolling against the ruler. If he had applied the ruler perfectly flat, it would have gone the other way. By tipping the ruler and applying leverage, he triggers the motion that is then maintained by the movement of the ruler.

Watch the video again - if he didn't tip the ruler slightly,it would have worked the other way.

rottenseedsays...

>> ^Throbbin:
It comes down to leverage. Notice how he tips the ruler while pushing it. This gets the round thing going in a certain way, and inertia keeps it rolling against the ruler. If he had applied the ruler perfectly flat, it would have gone the other way. By tipping the ruler and applying leverage, he triggers the motion that is then maintained by the movement of the ruler.
Watch the video again - if he didn't tip the ruler slightly,it would have worked the other way.

I disagree. It's a basic force/torque problem. The net force of the system was such that the system moves in the direction of the ruler. A simple force diagram should describe this.

10677says...

Rottenseed is right.

Think of it this way: If the net force on the cart system is applied to the right, then the system will accelerate to the right. For the cart to move right, the small wheels must rotate clockwise, and this motion must translate to the big wheel moving counter clockwise.

Floodsays...

In the instant the ruler is moved to the right while touching the top wheel, the force of friction between ruler and the wheel results in force applied to the top of the wheel pointing to the right. This results in a clockwise torque applied to the top wheel. The top wheel touches two smaller wheels which transfers the clockwise torque of the top wheel into counter-clockwise torque in the small wheels. The small wheels are touching the ground. The frictional force between the wheels and the ground work to resist movement. So when the small wheels have a counter-clockwise torque, the the frictional force resulting from the contact of the wheels and the ground is resulting in a force at the bottom of the small wheels but points to the left. This results in clockwise torque on the small wheels, which results in a counter-clockwise torque on the top wheel, which results in frictional force on the top of the top wheel point to the left.

So it all balances out right? Well, it would, if the size of all the wheels were the same.

Imagine what would happen if he held the ruler still but moved the table. You'll see that the direction of the surface (relative to the cart) near the larger wheel dictates the direction of the cart.

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