How Do You Calculate Angular Acceleration from Revolutions?

[gcombina]

A grindstone,initially at rest,is given a constant angular acceleration so that it makes 20.0 rev?
A grindstone,initially at rest,is given a constant angular acceleration so that it makes 20.0 rev in the first 8.00 s. What is its angular acceleration

Answer is 3.93 rad/s^2

My attempt:

α= Δω/ΔT

I converted 20 rev/8s to radians and I got 15.7 rad/s, then I plugged in the numbers into the equation above ^

α= 15.7 rad/s (wrong answer)

What am I doing wrong?

 

[CAF123]

What am I doing wrong?

Your work assumes that the stone moves at constant angular velocity.

 

[verty]

Draw a graph of radians versus time, that should help.

 

[Nathanael]

A grindstone,initially at rest,is given a constant angular acceleration so that it makes 20.0 rev in the first 8.00 s. What is its angular acceleration

You answered the question as if it said:
"A grindstone, initially at rest, is given a constant angular acceleration so that it is going 20.0 rev/s after the first 8.00 s"

See the difference?

 

[gcombina]

so i guess I should figure out the angular velocity first right?
such

ω = Θ/t

so later I do the other equation.

is this correct?

 

[gcombina]

so to solve for ω, i have

ω = Θ/t
= 20 (2∏) / (what should I put here in time if time wasn't given)

 

[dauto]

Use the equation for angular displacement in an angular accelerated motion. You don't have to waste time calculating angular velocities

 

[Nathanael]

so to solve for ω, i have

ω = Θ/t
= 20 (2∏) / (what should I put here in time if time wasn't given)

That would be average (not final) angular velocity.


Imagine the graph of the angular velocity over time. What is special about that graph? How can you use that to create an equation for the angular displacement?