My dad was driving in a highway, when we leave the highway there is a banked road. When car turning right, my body is leaning to the left. I thought my body will lean to the center due to centripetal force. Why??
[Physics] Why people lean right/left when turning left/right
centrifugal forcecentripetal-forceforcesnewtonian-mechanicsreference frames
Related Solutions
(1) is correct, but (2) and (3) are not. Consider a car turning counterclockwise around a track that is banked inwards. There are three forces acting on the vehicle: the weight of the car $\vec{W}$, the normal force $\vec{N}$, and the force of friction $\vec{f}$. Breaking these up into Cartesian coordinates gives:
$$\vec{W} = -mg\hat{y} \\ \vec{N} = N \left(\cos\phi \hat{y} - \sin\phi \hat{x}\right) \\ \vec{f} = f \left(-\sin\phi \hat{y} - \cos\phi \hat{x}\right)$$
Getting the direction correct for the friction is a bit subtle. We know from the $\phi \rightarrow 0$ limit that the friction has to point roughly in the direction of the turn, and also be perpendicular to the normal force, so for these coordinates, it must point down and to the left.
Since the car is moving in a circle in the horizontal plane, the forces in the $\hat{y}$ direction must cancel. Setting these equal to each other and considering the limiting case $f = \mu_s N$ gives an equation that can be solved for $N$. Then you can sum up the horizontal forces an insert this value to get the centripitel force.
You don't even need a banked road. The analogy of your orbit example would simply be a car moving at a constant speed in a circle (for simplicity we, for example, restrict to the case without skidding). In that case, there is no tangential force, and the force keeping the car in a circle is the force of static friction. We can see that this is possible in real life as follows. Let $m$ be the mass of the car, then a free body diagram shows that the normal force on the car has magnitude \begin{align} N = mg. \end{align} It follows that the force of static friction on the tires satisfies \begin{align} F_\mathrm s\leq \mu_\mathrm s N = \mu_\mathrm s mg \end{align} In other words, the force of static friction can have any value between $0$ and the product of the coefficient of static friction and the weight of the car.
Now, suppose that the car wants to drive in a circle of radius $r$. In this case, it will experience an acceleration with magnitude $v^2/r$ in the radial direction, and it will require a corresponding force \begin{align} F = \frac{mv^2}{r} \end{align} to do so. Since the force of static friction will be supplying this force, we require $F_\mathrm s = F$ which tell us that the car can move at a constant speed $v$ in a circle of radius $r$ without skidding provided \begin{align} \frac{v^2}{r}\leq \mu_s g. \end{align} It's easy to make this inequality satisfied; you just need to make sure that the circle has large radius, or the car has small speed, or some appropriate combination of the two.
Best Answer
There is centripetal force on the free upper part of your body, only to the extent it is attached to the lower part of your body, which is attached to the seat by friction and by the lap part of your seat belt. On the free upper part, there is centrifugal force which is caused by the inertia of the free upper part of your body tending to continue in a straight line as the car makes a turn to the right. Thus, the upper part of your body tends to lean left as the car turns right.
If it weren't for the friction of the car seat and the lap part of the seat belt, your entire body would tend to slide left as the car turns right. But your tether to the car causes you to seek the center of the arc being made by the car as it turns. Likewise, the friction of the car's tires on the road allow it to seek the center of the arc it makes, and to avoid flying off the road. Friction provides centripetal force, which overcomes the centrifugal force acting on the car and on you.
I'm assuming there is enough play in the upper part of the seat belt to allow you to lean somewhat toward the left. If there were a sudden acceleration to the right, the seat belt probably would clinch and prevent you from leaning left.
Centrifugal force is sometimes called a fictitious force, as it exists only in a rotating (accelerating in the sense of change of direction) reference frame. In an inertial reference frame free from acceleration, such as the world outside the car, centrifugal force doesn't exist.