Desperate! Circular motion - Acceleration and Velocity Analysis

[nns91]

Desperate ! Circular motion

Homework Statement

Particles travels counterclockwise in circles of radius 5m. The accleration vectors are indicated at three specific times. Find the values of v and dv/dt at each time.

a. a=20 m/s^2 . vector a points toward the center of the circle, vector v tangent to the circle

b. a=30 m/s^2. vector a points toward the center of the circle at a 30 degree angle in the direction of motion ( so imagine the case a, vector a point directly to the center, this case vector a and the vector a in part a creates a 30 degree)

c. a= 50 m/s^2. vector a creates a 45 degree angle clockwise with the radius.

Homework Equations

a=mv^2/s

The Attempt at a Solution

I know that it's confusing. Please give some input. if you guys are unclear I can explain more.

 

[tiny-tim]

Hi nns91!

(have a theta: θ )

I assume you know how to do a., using centripetal acceleration.

ok, for the others, you have the usual centripetal acceleration formula, and you also need to calculate the tangential acceleration (for constant r, that's a_t = rθ'' = v').

Acceleration is a vector, so you add accelerations just like velocities … add the centripetal and tangential accelerations, to get the required angle.

 

[nns91]

Thanks.

I know a_centripetal=mv²/2

The tangential part confuses me the most. How can I calculate it from that formula a_t=r$$\theta$$'=v' ??

What do you mean by to get the require angle ?

 

[tiny-tim]

Thanks.

I know a_centripetal=mv²/2

The tangential part confuses me the most. How can I calculate it from that formula a_t=r$$\theta$$'=v' ??

What do you mean by to get the require angle ?

Hi nns91!

(why didn't you use that θ i gave you? )

a_t = dv/dt, which you get from the question.

And if you want the total acceleration to be at 45º, for example, then obviously you need the centipetal acceleration to be equal to the tangential acceleration … just like adding velocities!

 

[nns91]

But I don't have time ? so how can I get dv/dt ?

 

[tiny-tim]

But I don't have time ? so how can I get dv/dt ?

Well, for 45º, for example, you need v²/r = dv/dt, so v = … ?

 

[nns91]

How about a 30 degree angle ?

 

[tiny-tim]

How about a 30 degree angle ?

Oi! Do it yourself!

 

[nns91]

I mean I still have not fully understand.

So they give a=20 m/s^2 in part a.

Thus: v=sqrt(ar)= sqrt(20*5)= 10 m/s

Is that right ??

I still don't understand the calculation of acceleration

 

[tiny-tim]

So they give a=20 m/s^2 in part a.

Thus: v=sqrt(ar)= sqrt(20*5)= 10 m/s

Is that right ??

That's right.

Now try c.

 

[nns91]

c.

v= sqrt(a*r)=sqrt(50.5)= 15.8 m/s ??

So I got v.

How then can I calculate dv/dt ?