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1. Mar 18, 2017

### Faiq

1. The problem statement, all variables and given/known data

2 A particle P of mass mkg moves on an arc of a circle with centre O and radius a metres. At time t = 0
the particle is at the point A. At time t seconds, angle POA = sin^2 2t.
Find
(i) the value of t when the transverse component of the acceleration of P is first equal to zero

The answer is $$\frac{d^2\theta}{dt^2} = 0$$
Isn't d^2theta/dt^2 equal to radial acceleration. Since angular velocity is rate of change of theta, thus rate of change of change of theta should be angular acceleration aka radial acceleration?
Then why are the equating it as transverse component?

2. Mar 18, 2017

### FactChecker

If P goes around in a circle, the velocity vector is always at right angles to the radius through P. So the radial and transverse acceleration are equal.

3. Mar 18, 2017

### Faiq

In the next part, we are supposed to calculate radial force and transverse force and the answer is 3ma and 4ma respectively. If they are both equal then the force due to their acceleration should be same as well

4. Mar 18, 2017

### Staff: Mentor

The radial acceleration is $v^2/a$, where v is the instantaneous tangential velocity. When they are talking about transverse acceleration, it think they mean tangential acceleration.

5. Mar 18, 2017

### Faiq

I went through a post on a different website which acquired the following relation. Is it correct?
$$\frac{d}{dt}v=r\frac{d}{dt}\omega$$
$$a_t=ra_r$$

6. Mar 18, 2017

### Staff: Mentor

The first equation is correct. The second isn't.

7. Mar 18, 2017

### Faiq

Why? I dont see anything wrong with the equation?

8. Mar 18, 2017

### Staff: Mentor

What!!!!???? Since when is $a_r=\frac{d\omega}{dt}$????

9. Mar 18, 2017

### Faiq

10. Mar 18, 2017

### Staff: Mentor

$a_r$ is the conventional symbol for radial acceleration. The conventional symbol for angular acceleration is $\alpha$. If you are going to use unconventional symbols, you need to make that clear.

11. Mar 18, 2017

### Faiq

Is there a difference between radial, angular and centripetal acceleration for a circular motion? In our class, we used them interchangeably

12. Mar 18, 2017

### Staff: Mentor

Let me understand this correctly: In your class, they think that radial acceleration is the same thing as angular acceleration? Actually, they are entirely different quantities. The correct equation for radial acceleration is $a_r=\omega ^2r$ and angular acceleration is $\alpha=\frac{d\omega}{dt}$. They don't even have the same units.

13. Mar 18, 2017

### Faiq

So
but
angular acceleration = tangential acceleration / radius.

14. Mar 18, 2017

### Staff: Mentor

For.a circular arc, yes.

15. Mar 18, 2017

### Faiq

Okay thank you