Confusion regarding centripetal acceleration and tangential acceleration

[tellmesomething]

Homework Statement

This isn't a homework question but I am in high school so my doubts are most befitting in threads like this I suppose

Relevant Equations

I wanted to know how the trajectory of motion of a particle moving only initially with centripetal acceleration would change after acquiring tangential acceleration. Maybe you can cite two side by side examples or a before and after situation of a particle, anything would help greatly.

I do not understand enough.

 

[haruspex]

It depends what you mean by "acquiring tangential acceleration". That involves a force, but how is this force acting over time? Does it continue to be aligned with the velocity of the particle, or act in a fixed direction or some other way?
Also, the initial centripetal acceleration necessitates a force. How will that react?

 

[tellmesomething]

isnt the force acting inwardly towards the centripetal acceleraation, why would it be aligned with the velocity ? considering there is no other acceleration i.e the first case of my question.

My main motive with this was to find out if tangential acceleration helps the object move translationally by any chance, i think im very wrong but i am just confused if any of these centripetal, tangential or radial acceleration help it move forward.

For ex the tyre of a bicycle rotates and moves forward, each particle on the circumference have centripetal acceleration, and tangential acceleration (considering im speeding up), what acceleration provides the forward movement or more correctly what force? Is this my i.e the rider's provided force? Or is it a component of the force which help the tyre rotate,

im sorry if this seems confusing to read im not even sure i know what im asking but im just confused as i know the net force causes the acceleration in its direction but here we have centripetal tangential and forward acceleration all arising from the same force?

 

[kuruman]

Homework Statement: This isn't a homework question but I am in high school so my doubts are most befitting in threads like this I suppose

For future reference, if your doubts are not directly related to a homework problem, they should be posted elsewhere. This particular thread most appropriately befits the "Classical Physics" forum. It is understandable, however, that you are new here, so no harm done.

That said, you need to understand that the centripetal and tangential acceleration are always perpendicular to each other and affect the motion of an object differently. The two together are components of the acceleration vector. The tangential component is responsible for changing the speed but not the direction of the velocity whilst the centripetal component is responsible for changing the direction of the velocity but not the speed.

The rules are:

• If the tangential component is in the same direction as the velocity, the speed increases.
• If the tangential component is in the opposite direction as the velocity, the speed decreases.
• If the centripetal component is perpendicular and points to the left of the velocity, the object veers to the left.
• If the centripetal component is perpendicular and points to the right of the velocity, the object veers to the right.

Specific example
The driver of a car gets the car to go where he pleases by controlling the tangential and centripetal components of its acceleration:

• The accelerator pedal provides a tangential component in the same direction as the velocity as determined by the gear setting (forward or reverse).
• The brake pedal provides a tangential component in the opposite direction as the velocity regardless of gear setting.
• The steering provides a centripetal component to the right or to the left as needed.

Consider a driver entering a right hand turn in a city street.

1. He applies the brake thus reducing the speed and turns the wheel to the right. This causes the car to slow down and start turning to the right.
2. Halfway into the turn he eases off the brake while the wheel is still turned. This causes the car to move at a slow constant speed while still turning.
3. Near the exit of the turn, he applies the accelerator while the wheel is still turned. This causes the car to speed up while still turning.
4. Finally, he straightens the wheel to make the car move in a straight line that is perpendicular and to the right of his original direction.

I think you can now answer your own question, "I wanted to know how the trajectory of motion of a particle moving only initially with centripetal acceleration would change after acquiring tangential acceleration." Just imagine a car going around in a circle a constant speed suddenly when suddenly the driver pushes on the accelerator pedal keeping the steering wheel steady.

 

[tellmesomething]

The rules are:

• If the tangential component is in the same direction as the velocity, the speed increases.
• If the tangential component is in the opposite direction as the velocity, the speed decreases.
• If the centripetal component is perpendicular and points to the left of the velocity, the object veers to the left.
• If the centripetal component is perpendicular and points to the right of the velocity, the object veers to the righ

Hi, first of all sorry for the wrong thread post, i will make note of that. I definitely have a lot of questions, i think i had some very wrong intution about this topic. Here is the centripetal component pointing left or right of the velocity vector indicative of the change in direction of the velocity vector ? I have learned that the centripetal component always points towards the center

secondly as you mention below in your post that the accelerator provides a tangential component are you trying to say that the tangential component helps the car move forward as in it makes it move translationally? I thought it helps the tyre rotate ( im sorry if this is some kind of gibberish)?

Again I am sorry if this makes no sense im truly very confused so i dont think i can even formulate questions on my doubt

 

[gmax137]

For ex the tyre of a bicycle rotates and moves forward, each particle on the circumference have centripetal acceleration, and tangential acceleration (considering im speeding up), what acceleration provides the forward movement or more correctly what force?

The force you're looking for is the friction between the tire and the ground. If you tried to pedal on slick ice, what would happen?

Wheels and how they work is more complicated than it seems at first glance, and many people are confused by this.

 

[tellmesomething]

The force you're looking for is the friction between the tire and the ground. If you tried to pedal on slick ice, what would happen?

Wheels and how they work is more complicated than it seems at first glance, and many people are confused by this

Hi thanks for the reply. On slick ice i think tyres wouldn't turn? would they slide off in the backward direction?? Also someone said before you that the accelerator of a car provides tangential component of acceleration for the car, and that is true so is this a different way of defining tangential acceleration?

 

[gmax137]

Ideally, you would pedal and the [EDIT] back tire would spin. You and the bike remain in the same spot.

 

[tellmesomething]

Ideally, you would pedal and the tires would spin. You and the bike remain in the same spot.

Gah! Okay one more fundamental concept i do not understand. Sorry i will look into rolling friction asap.

 

[tellmesomething]

In this case there can be tangential acceleration yes? I mean to say we can get frustrated and pedal faster? Also i edited my post if you're available please check it out

 

[tellmesomething]

Also i know these are continous replies but wanted to tell you that it makes so much sense for friction to be the one helping us forward in a car. No wonder when someone moves on their legs they feel tired because they are expending the energy in a car oh no boy. Physics is amazing.

 

[tellmesomething]

Ideally, you would pedal and the [EDIT] back tire would spin. You and the bike remain in the same spot.

Also i know these are continous replies but wanted to tell you that it makes so much sense for friction to be the one helping us forward in a car. No wonder when someone moves on their legs they feel tired because they are expending the energy in a car oh no boy I aint doing the work. Physics is amazing.

 

[kuruman]

I have learned that the centripetal component always points towards the center

You learned correctly. If a car moves forward and turns right at the same time, the centripetal acceleration points to the right of the driver. The car itself describes an arc of a circle. The center of the circle is to the right of the driver.

secondly as you mention below in your post that the accelerator provides a tangential component are you trying to say that the tangential component helps the car move forward as in it makes it move translationally? I thought it helps the tyre rotate ( im sorry if this is some kind of gibberish)?

The fact that the tires rotate and propel the car forward is only incidental. The end result of pushing on the accelerator pedal is that the speed of the car increases in the forward direction. According to the rules in post #4, that means that there is a component of the acceleration in the same direction as the velocity and therefore the speed in the forward direction increases.

 

[haruspex]

way of defining tangential acceleration?

Tangential acceleration is defined as that component of the overall acceleration which is parallel to the velocity; centripetal acceleration is defined as that component of the overall acceleration which is normal to the velocity.

Many get confused about centripetal force, taking it to be a particular one of the applied forces, or even an extra force.
At any instant, many forces may act on a body. The (vectorial) sum of these is the net force and produces the overall acceleration. The component of the net force which is normal to the (instantaneous) velocity produces the centripetal acceleration, so is known as the centripetal force.

Another source of confusion is that students are initially given scenarios where the radius and centre of rotation do not change, so get the false impression that centripetal acceleration only refers to cases where the centre of the rotation is fixed. A projectile describing a parabolic arc undergoes both centripetal and tangential acceleration. The overall acceleration, $\vec g$, is constant, but its angle to the velocity vector keeps changing, so how it splits into tangential and centripetal components keeps changing, and the centre of the rotation keeps changing. (Challenge: find the locus of the centre of rotation.)