# Tangential acceleration and centripetal acceleration

• siapola1
In summary, a disc with a radius of 16cm starts spinning from rest with a uniform angular acceleration of 8.0 rad/s^2. The tangential acceleration is 50 m/s^2 and the centripetal acceleration is 2.56 m/s^2. The formula for centripetal acceleration is incorrect and the correct formula is √((rω2)2+(αr)2) = r√(ω4+α2). The centripetal and tangential accelerations are at right angles and the total acceleration has a magnitude of r√(ω4+α2).
siapola1
a disc or radius r = 16cm starts spinning from rest with a uniform angular acceleration of 8.0 rad/s^2. at what time is its tangential acceleration twice the centripetal acceleration.

i figured out the tangential acceleration is:
Atan = α/R = 8 / .16 = 50 m/s^2

and the centripetal acceleration is :
2(α*R) = 2.56 m/s^2then i got stuck. will the centripetal increase as its tangential acceleration increase?

siapola1 said:
Atan = α/R
Not a good start.
siapola1 said:
2(α*R) = 2.56 m/s^2
That's a better attempt at the tangential acceleration, but not quite right.
Can you find a correct formula for centripetal?

haruspex said:
Not a good start.
So can you help me please?

siapola1 said:
So can you help me please?
Don't you have any notes or textbook that give you the relationship between angular and tangential accelerations?
What about angular and tangential velocities? Angular and tangential displacements?

I wasnt in class that day and homework are usually much harder than lectures.
He gave is us this formula in class

Centripetal acc. = R * (ω4 + α2)
But I don't know how to use it in this problem

siapola1 said:
I wasnt in class that day and homework are usually much harder than lectures.
He gave is us this formula in class

Centripetal acc. = R * (ω4 + α2)
But I don't know how to use it in this problem
Oh. That's not helpful at all. In fact it is wrong.
If the angular acceleration is α, radius r, then the tangential acceleration is αr.
Likewise, if a disc is rotated by angle θ then a point on its rim travels an arc length θr, and if rotating at rate ω then the tangential velocity is ωr.
The centripetal acceleration is that component of the total acceleration which is normal to the velocity. For a rotating disc it is pointing towards the disc's centre. Its magnitude is v2/r = rω2.
The centripetal and tangential accelerations are at right angles, so the total acceleration has magnitude √((rω2)2+(αr)2) = r√(ω42).

Delta2

## 1. What is tangential acceleration?

Tangential acceleration is a measure of the rate at which the magnitude and direction of an object's velocity changes as it moves along a curved path. It is the component of acceleration that is parallel to the object's velocity vector.

## 2. How is tangential acceleration different from centripetal acceleration?

Tangential acceleration and centripetal acceleration are often confused, but they are actually two different components of an object's overall acceleration. While tangential acceleration is parallel to the object's velocity, centripetal acceleration is perpendicular to the velocity and directed towards the center of the curved path.

## 3. What causes centripetal acceleration?

Centripetal acceleration is caused by a centripetal force, which is any force that directs an object towards the center of a circular path. This force is necessary to keep an object moving along a curved path instead of moving in a straight line.

## 4. How is centripetal acceleration calculated?

Centripetal acceleration can be calculated using the formula a = v²/r, where a is the centripetal acceleration, v is the velocity of the object, and r is the radius of the curved path. This formula can also be written as a = ω²r, where ω is the angular velocity of the object in radians per second.

## 5. What are some real-life examples of tangential and centripetal acceleration?

Tangential acceleration can be observed in a car moving along a curved road, as the car's speed and direction of motion change. Centripetal acceleration can be seen in the motion of a satellite orbiting around the Earth, as the gravitational force from the Earth constantly pulls the satellite towards the center of its orbit.

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