# Direction of static friction between a vehicle and circular dome

• alyssam042
In summary: I think I answered that already.The body's acceleration is in the direction of the centripetal force.
alyssam042
Homework Statement
Someone is riding a motorcycle in horizontal circles inside the surface of a large dome with radius R. They have a constant velocity v, and are located at angle θ above the ground. Draw a free body diagram including static friction.
Relevant Equations
None
So the only problem I am having is determining the direction of static friction. I did the same problem but while they were going in a vertical circular motion instead, where the static friction force was in the direction of centripetal force (pointing to the center of the circle).

Would it be the same in this case as well? Since the motorcycle is not going in a horizontal circular motion at the center of the dome, I have the normal force pointed perpendicular to the surface like normal. But what about the static friction?

alyssam042 said:
going in a vertical circular motion instead, where the static friction force was in the direction of centripetal force (pointing to the center of the circle).
I fail to see how the static friction, which is necessarily tangential, could ever point radially.
alyssam042 said:
determining the direction of static friction
Please be specific about what possibilities you think you have narrowed it down to.

scottdave
haruspex said:
I fail to see how the static friction, which is necessarily tangential, could ever point radially.

Please be specific about what possibilities you think you have narrowed it down to.
From what I understand, the static friction is usually what "supplies" the centripetal force, and causes radial acceleration.

I do not have it narrowed down to much unfortunately, I'm not sure if it would be normal to the path or just completely parallel to the path of the dome possibly.

Here is a diagram if that helps

Lnewqban
alyssam042 said:
Here is a diagram if that helps
That is a diagram. It is not a "free body diagram" since it does not show any forces.

alyssam042 said:
I did the same problem but while they were going in a vertical circular motion instead, where the static friction force was in the direction of centripetal force (pointing to the center of the circle).
I think you are confusing the normal force and the force of static friction. In the vertical circle problem it is the normal force that provides the centripetal acceleration. By definition, the force of static friction is always parallel to the surface and the normal force is perpendicular and away from the surface. Can you add these two forces plus gravity in your drawing to address the issue that @jbriggs444 brought up in post #5? Drawing gravity and the normal force first should help you figure out how to draw the force of static friction.

PeroK
jbriggs444 said:
That is a diagram. It is not a "free body diagram" since it does not show any forces.
I know. That is just a diagram the HW problem gave me, which is why I called it a diagram, not a free body diagram.

PeroK
alyssam042 said:
From what I understand, the static friction is usually what "supplies" the centripetal force, and causes radial acceleration.
I can think of a situation like that, but I don’t think I've ever seen it in a physics exercise.
alyssam042 said:
I know. That is just a diagram the HW problem gave me
This forum requires that you show some attempt, so draw a free body diagram of the motorcycle-and-rider 'rigid' body, then try to answer as many of these questions as you can:

What forces act on it?
What are the directions of those forces, as far as you can determine?
If the motorcycle were on a level road, what would be the possible directions for friction between tyre and road?
What is the body’s acceleration (magnitude and direction)?

Last edited:
PeroK
haruspex said:
I can think of a situation like that, but I don’t think I've ever seen it in a physics exercise.
Car going around in a circle on a flat horizontal surface at constant speed?

haruspex
kuruman said:
Car going around in a circle on a flat horizontal surface at constant speed?
Doh!

## What is the direction of static friction when a vehicle is at rest on a circular dome?

The direction of static friction when a vehicle is at rest on a circular dome is tangential to the surface of the dome. It acts to prevent the vehicle from sliding down due to gravity, opposing the component of gravitational force parallel to the surface.

## How does the direction of static friction change as the vehicle moves on the circular dome?

As the vehicle moves on the circular dome, the direction of static friction continuously adjusts to remain tangential to the dome's surface and opposite to the direction of any potential sliding motion. This ensures that the vehicle maintains its path without slipping.

## What factors determine the magnitude and direction of static friction on a circular dome?

The magnitude and direction of static friction on a circular dome are determined by the vehicle's weight, the angle of the dome's surface at the point of contact, and the coefficient of static friction between the vehicle's tires and the dome's surface. The frictional force must counteract the component of gravitational force parallel to the surface to prevent slipping.

## Can static friction act upwards on a vehicle on a circular dome?

Yes, static friction can act upwards on a vehicle on a circular dome if the vehicle is positioned such that the component of gravitational force along the surface is directed downwards. In this case, static friction acts upwards along the surface to prevent the vehicle from sliding down.

## How does the curvature of the dome affect the static friction experienced by the vehicle?

The curvature of the dome affects the static friction experienced by the vehicle by altering the angle of the surface relative to the horizontal. A steeper curvature increases the component of gravitational force parallel to the surface, requiring greater static friction to prevent slipping. Conversely, a gentler curvature reduces this component, requiring less static friction.

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