What is the average angular speed of the grindstone?

[brncsfns5621]

Homework Statement

A grindstone of radius 4.0m is initialy spinning with an angular speed of 8.0 rad/s. The angular speed is the increased to 10rad/s over the next 4.0 seconds. Assume that the angular acceleration is constant. What is the average angular speed of the grindstone?

Homework Equations

Please check work...

The Attempt at a Solution

avg w= (delta theta)/delta T
= (10 rad/s - 8 rad/s) / (4 s-0)
= .5 rad/s

Vt= r * avg w
= 4m * .5 rad/s
= 2 rad/s

 

[Doc Al]

What you calculated is the average angular acceleration, not the average angular speed. (Even though your equation was correct--change in theta over time--what you put into the equation was change in angular speed over time. You might have caught the error if you checked your units.)

Sanity check: If it starts at 8 rad/s and speeds up to 10 rad/s--how can the average speed be only 2 rad/s?

 

[brncsfns5621]

This is where I get confused with Physics. Are speed and velocity the same thing?

Redoing the math, which I hope is right:

Avg speed is (10 rad/s + 8 rad/s) / 4 s = 4.5 rad/s

Vt = r*w = 4 m * 4.5 rad/s = 18 rad/s

Or do I not need to go as far to find Vt?

 

[e(ho0n3]

Velocity is a vector while speed is a scalar quantity. Always keep that in mind.

 

[brncsfns5621]

I think I found it in the textbook:

Since the angular acceleration is constant:
Avg ang velocity= 1/2[wo + w] = 1/2[8+10]= 9 rad/s

 

[Mentz114]

I assume the question is asking for the average angulat speed during the 4s of acceleration. To get this, you need to calculate how far it turns ( in radians) and divide by 4s.

Remember this

distance = 1/2 * acceleration * time^2

for linear motion.

So for angular motion

angle turned = 1/2 * ang. acc. * time^2

Do you follow ?

 

[Doc Al]

Avg speed is (10 rad/s + 8 rad/s) / 4 s = 4.5 rad/s

Again, this equation fails the "common sense" test. You start out at 8 rad/s and end up at 10 rad/s--so don't you think the average speed must be somewhere in the middle of those two speeds?

And the units don't match--you divide by time, but still your answer is in rad/s. (Dividing rad/s by s gives you units of rad/s^2--which are the wrong units for angular speed.)

I think I found it in the textbook:

Since the angular acceleration is constant:
Avg ang velocity= 1/2[wo + w] = 1/2[8+10]= 9 rad/s

Now you've got it.