Rotational Dynamics Homework: Velocity & Acceleration of Wheel

[lukatwo]

Homework Statement

A wheel is spinning at n=1200rpm. The wheel starts to linearly decelerate, and after t=100s it stops. Determine the velocity, and acceleration of a point 10cm from the center of the mass, after 50 seconds of decelerating. The radius of the wheel is 30cm.

Homework Equations

Since the wheel is spinning without sliding $v=ωr$

$ω=n{\frac{2∏}{60}}$

$a_{CM}=ωα$

The Attempt at a Solution

I'm generally having a problem of understanding the relations between all the different velocities, and accelerations. I can determine the angular velocity, but am pretty much lost from thereon out.

 

[BvU]

You need to explain a bit more about the variable names you use, in the equations in particular: what is a_CM ? Don't see it anywhere else.

Your attempt at a solution is not.

My diagnose is: read up in your notes and in your textbook or on the web (wiki or hyperphysics).

It's not rocket science (although...) and there are a lot of analogies with linear motion.

Re "pretty much lost": come on. They tell you 1200 rpm linearly goes to 0 rpm in 100 s. What would it be after 50 s ?
And you know how to convert rpm to angular speed. You have another useful equation and presto: there's your velocity. Acceleration is a bit more involved, but I'm not going to spoonfeed that until you have read up on the subject. Probably won't have to anymore then anyway. Good hunting!

 

[lukatwo]

Thanks, in the absence of an answer I've reread my notes, and managed to solve the problem. I've had to put everything in it's place in my head(all the different accelerations, and velocities). English is obviously not my mother language so I probably got the terminology part wrong.

 

[BvU]

Still glad you could work your own way through this!

 

[HalfLostAndSearching]

I would recommend breaking down the problem into smaller components and using the equations provided to solve for each one individually. First, you can calculate the angular velocity (ω) using the given rotational speed (n). Then, you can use the equation v=ωr to determine the linear velocity (v) of the point 10cm from the center of mass. From there, you can use the given time (t) and the final linear velocity (v) to calculate the deceleration (a) using the equation a = (vf - vi)/t. Finally, you can use the equation a=ωα to solve for the angular acceleration (α).

It may also be helpful to draw a diagram to visualize the problem and the different components involved. Additionally, you can refer to your textbook or class notes for more information on rotational dynamics and the relationships between different velocities and accelerations in a spinning object.