# Rotation with a turntable

1. Feb 16, 2015

### thegoosegirl42

I know this is not typical and you aren't suppose to solve the problem for the person just give hints, however my teacher has not taught this and expects us to know it. For whatever I cannot grasp how to do this any help would be great thank you!

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

The turntable of a record player has an angular speed of 3.5 rad/s at the instant it is turned off. The turntable stops 1.6s after being turned off. The radius of the turntable is 15cm. (a) If the angular acceleration is constant, through how many radians does the turntable turn after being turned off? (b) What is the magnitude of the linear acceleration of a point on the rim of the turntable 1.0s after it is turned off? (Hint: The linear acceleration has both a radial and a tangential component).

2. Relevant equations
We have not been given any equations yet, we were just told to use the position function and ones used in projectile motion problems.

3. The attempt at a solution
for a I got 4.375 I took 3.5(1.6/2). Is this right? I don't really have any reasonings for why I did it. I don't understand how to do b. If you could send me down the right path with that one it would be greatly appreciated.

2. Feb 16, 2015

### Staff: Mentor

The equations for rotational motion have a one-to-one correspondence with those for kinematics, just the variable names change.

Convert the "story" to linear motion terms so that you can think about it on familiar grounds:

An object has a linear speed of 3.5 m/s at the instant it is released on a flat surface. It coasts to a stop 1.6 second after being released. If the acceleration is constant, what is the distance it traveled after release?

3. Feb 17, 2015

### thegoosegirl42

Thank you very much that helped me with a but how do I even approach b this is where I was really thrown through the loop. I tried to find the velocity at 1 s with no success.

4. Feb 17, 2015

### Staff: Mentor

Did you calculate the angular acceleration while answering part (a)?

5. Feb 17, 2015

### thegoosegirl42

Would that be the acceleration divided by the radius?

6. Feb 17, 2015

### Staff: Mentor

Well, yes, it would be equal to the tangential acceleration divided by the radius. I thought you might have determined it from the initial and final angular velocities and the stopping time. It'll come in handy for writing the equation of motion for the turntable w.r.t. time.