Tangential acceleration, linear acceleration, and torque

[blueblast]

What is the difference between tangential and linear acceleration of a circular object (let's say a ball)? Also, how does the torque contribute to linear acceleration?

 

[BvU]

What did you find during your quest on the net ?

 

[blueblast]

What did you find during your quest on the net ?

Not much.

 

[Chandra Prayaga]

Let us start from the definitions. What is linear acceleration, and what is angular accelertion? Also, at what level are you looking at the topic, calculus based physics, or algebra based physics?

 

[BvU]

Not much.

Is an answer to the question how much did you find...", not to the question "what did you find" ...

Let me rephrase: what search terms did you use and which results did you like, which did you not like ?

Reason I ask is that I have no idea what level of answer I can give. Do you already know what the terms stand for, and want something specific on a spherical object (a ball is not a circular object) ?

 

[shrey012]

Tangential and radial acceleration are both types of linear acceleration. Tangential acceleration is the rate of change of the tangential velocity and arises when the speed around the circle is not constant; radial acceleration will always be present (including for constant speeds) and points to the centre of the circle. The other type of acceleration would be angular acceleration.

Now, let's explore how exactly the torque affects the tangential acceleration.

$$\tau = \frac{d(Iw)}{dt} = I \frac{dw}{dt}$$ We know this because the net torque is equal to the rate of change of angular momentum.
So $$\frac{dw}{dt} = \frac{\tau}{I}$$
$$\frac{dv}{dt} = \frac{d(wr)}{dt} = r \frac{dw}{dt} = r \frac{\tau}{I}$$

Here, v represents tangential velocity, which is equivalent to wr.