Centripetal acceleration and tangential acceleration

• Maxo
In summary, the conversation discusses the difference between tangential acceleration and centripetal acceleration in circular motion. The tangential acceleration depends on both the initial and final angular velocity, while the centripetal acceleration only depends on the final angular velocity. This is because the centripetal acceleration is constantly changing in direction to maintain circular motion, while the tangential acceleration remains constant in direction.
Maxo
When having a circular acceleration motion, we have both tangential acceleration and centripetal acceleration.

The tangential acceleration is aT=r*α where α=1/2*(ωf0). So we can see tha aT is dependant on both the initial angular velocity ω0 and the final ωf).

For centripetal acceleration, we instead have aC=r*ωf2.

My question is, how come the centripetal acceleration is only dependant on the final angular velocity, and not the initial?
Is there a physical explanation for this?

First: α isn't 1/2*(ωf0). The correct equation is α = (ωf0)/(tf-t0).

Second: The equation above is the expression for the AVERAGE angular acceleration. If the circular motion is UNIFORMLY accelerated than you can use the average angular acceleration to calculate the tangential speed since angular acceleration is constant, otherwise you have to use the instantaneous angular acceleration - say αf and the expression for tangetial acceleration becomes aTf = r αf

Ok thanks for the correction. But I still wonder why the centripetal acceleration is only dependant on the final angular velocity, and not the initial angular velocity. Is there a physical explanation for this?

centripetal acceleration is caused to continue circular motion so at every point. so at that point it has to accelerate the mass toward center so as to change it direction.
now for at the point it has angular velocity omega then centripetal acceleration will vary with that only

I can explain the difference between tangential and centripetal acceleration and why they are dependent on different variables.

First, let's define what these two types of acceleration are. Tangential acceleration is the rate of change of tangential velocity, which is the velocity along the circular path. This means that tangential acceleration is responsible for changing the speed of an object moving in a circular path. On the other hand, centripetal acceleration is the acceleration towards the center of the circular path. It is responsible for keeping the object moving in a circular path by constantly changing its direction.

Now, let's look at the equations for tangential and centripetal acceleration. As you mentioned, tangential acceleration is given by aT = r*α, where r is the radius of the circular path and α is the angular acceleration. This equation tells us that tangential acceleration is dependent on both the radius of the circle and the angular acceleration.

On the other hand, centripetal acceleration is given by aC = r*ωf^2, where ωf is the final angular velocity. This equation shows us that centripetal acceleration is only dependent on the final angular velocity and not the initial. This is because, in a circular motion, the final angular velocity is the same as the initial velocity, since the object is constantly moving at a constant speed along the circular path.

To understand why this is the case, we need to look at the forces acting on the object. In circular motion, there are two main forces at play - tangential force and centripetal force. The tangential force is responsible for changing the speed of the object, while the centripetal force is responsible for changing its direction.

When an object starts moving in a circular path, there is no tangential force acting on it, and the only force is the centripetal force. This force is what causes the object to move in a circular path. As the object moves, the tangential force increases, and the centripetal force decreases until they reach a balance, and the object moves at a constant speed along the circular path. This is why the final and initial angular velocities are the same, and the centripetal acceleration is only dependent on the final velocity.

In conclusion, the difference in the dependence of tangential and centripetal acceleration on initial and final angular velocities can be explained by the forces acting on the object in circular motion. While tang

What is centripetal acceleration?

Centripetal acceleration is the acceleration experienced by an object moving in a circular path. It always points towards the center of the circle and is caused by the centripetal force acting on the object.

What is tangential acceleration?

Tangential acceleration is the acceleration experienced by an object moving in a curved path. It is always tangent to the curve and is caused by changes in the object's speed or direction of motion.

How are centripetal acceleration and tangential acceleration related?

Centripetal acceleration and tangential acceleration are both components of the total acceleration that an object experiences while moving in a curved path. Centripetal acceleration is responsible for keeping the object moving in a circular path, while tangential acceleration is responsible for changes in the speed or direction of the object.

What is the difference between centripetal acceleration and centrifugal acceleration?

Centripetal acceleration is the acceleration towards the center of the circle that an object experiences while moving in a curved path, while centrifugal acceleration is the apparent outward acceleration experienced by an object in a circular motion. Centrifugal acceleration is actually just an inertial force and does not actually exist as a true acceleration.

How is centripetal acceleration calculated?

Centripetal acceleration can be calculated using the formula a = v^2/r, where a is the centripetal acceleration, v is the speed of the object, and r is the radius of the circular path. This formula can also be written as a = ω^2r, where ω is the angular velocity of the object.

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