What is the average angular speed of the grindstone?

Here, the units work out--you have rad/s on each term, so the result is in rad/s. And it's reasonable (and matches the answer in the back of the book).The reason you can't use the average speed formula is that the angular acceleration is not constant. So you can't use the average speed formula at all. (And if the problem is asking something else, then we need to see the problem.)Oh, ok. I think I get it now. Thank you for the clarification.In summary, the grindstone of radius 4.0m initially has an angular speed of 8.0 rad/s and increases to 10 rad/s over the next 4.0
  • #1
brncsfns5621
22
0

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
 
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  • #2
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? :wink:
 
Last edited:
  • #3
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?
 
  • #4
Velocity is a vector while speed is a scalar quantity. Always keep that in mind.
 
  • #5
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
 
  • #6
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 ?
 
  • #7
brncsfns5621 said:
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.)

brncsfns5621 said:
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. :smile:
 

1. What is average angular speed?

The average angular speed is a measure of how fast an object is rotating around a fixed point. It is defined as the change in angular position over a certain period of time.

2. How is average angular speed calculated?

Average angular speed is calculated by dividing the change in angular position by the change in time. This is represented by the formula: ω = Δθ/Δt, where ω is the average angular speed, Δθ is the change in angular position, and Δt is the change in time.

3. What are the units of average angular speed?

The units of average angular speed depend on the units used for angular position and time. Common units include radians per second (rad/s) and revolutions per minute (rpm).

4. How does average angular speed differ from instantaneous angular speed?

Average angular speed is calculated over a certain period of time, while instantaneous angular speed is the speed of an object at a specific moment in time. Average angular speed takes into account changes in speed over time, while instantaneous angular speed only gives the speed at a single point.

5. What factors can affect the average angular speed of an object?

The average angular speed of an object can be affected by factors such as the size and shape of the object, the distance from the fixed point it is rotating around, and any external forces acting on the object.

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