A circular saw blade rotating at 3600 rpm is braked to a stop in 6 seconds. What is the angular acceleration? How many revolutions did the blade make before coming to a stop?

Initial angular velocity = wo

= 3600*(2 pi)/60 = 377 rad/s
Angular acceleratiom = -wo/t
= -62.8 rad/s^2

Number of revolutions = (average angular velocity*t/(2 pi)
= (1/2)(377)*t/(2 pi) = 180
or average rpm*(1/10 minute)
= 3600*(1/2)*1/10)= 180

Well, let's saw through this math problem together, shall we? Now, we know that the blade started at 3600 rpm (revolutions per minute) and came to a stop in 6 seconds. To find the angular acceleration, we can use the formula:

angular acceleration = (final angular velocity - initial angular velocity) / time

Since the blade came to a stop, the final angular velocity is 0. The initial angular velocity is given as 3600 rpm, but we need to convert that into radians per second to match the units of the other values.

So, 3600 rpm can be converted to (3600 * 2π) / 60 rad/s, which is approximately 376.99 rad/s.

Using the formula, we have:

angular acceleration = (0 - 376.99 rad/s) / 6 s

Calculating that, we get around -62.83 rad/s² as the angular acceleration. Now, let's move on to the number of revolutions the blade made before coming to a stop.

To find the number of revolutions, we need to consider that the blade started at 3600 rpm and came to a stop. In 6 seconds, it has gone through a certain number of revolutions. We can use the formula:

number of revolutions = (initial angular velocity * time) / 2π

Plugging in the values, we get:

number of revolutions = (376.99 rad/s * 6 s) / 2π

After the calculation, we find that the blade made approximately 36.02 revolutions before coming to a stop.

So, the angular acceleration is -62.83 rad/s², and the blade made around 36.02 revolutions. I hope I didn't saw you with too much information there!

To find the angular acceleration, we can use the equation:

Angular acceleration (α) = (Change in Angular velocity)/(Time taken)

The circular saw blade is rotating at an initial angular velocity of 3600 rpm, which is equal to 3600/60 = 60 revolutions per second.

The final angular velocity is 0, since the blade comes to a stop.

The time taken is given as 6 seconds.

Change in angular velocity = final angular velocity - initial angular velocity = 0 - 60 rev/s = -60 rev/s

Angular acceleration (α) = (-60 rev/s)/(6 s) = -10 rev/s^2

Therefore, the angular acceleration is -10 rev/s^2.

To find the number of revolutions the blade made before coming to a stop, we can use the equation:

Number of revolutions = (Initial angular velocity * Time taken) + (0.5 * Angular acceleration * Time taken^2)

Substituting the known values:

Number of revolutions = (60 rev/s * 6 s) + (0.5 * -10 rev/s^2 * (6 s)^2)

Number of revolutions = 360 rev + (0.5 * -10 rev/s^2 * 36 s^2)

Number of revolutions = 360 rev - 180 rev

Number of revolutions = 180 rev

Therefore, the blade made 180 revolutions before coming to a stop.

To find the angular acceleration, we can use the formula:

angular acceleration (α) = Δangular velocity (ω) / time (t)

Given that the circular saw blade is rotating at 3600 rpm and is braked to a stop in 6 seconds, we need to convert the initial angular velocity from rpm to radians per second.

1 revolution = 2π radians

Therefore, the initial angular velocity (ω) can be calculated as follows:

initial angular velocity (ω) = 3600 rpm * (2π radians / 1 revolution) * (1 minute / 60 seconds)

Now, we can calculate the angular acceleration:

α = (0 rad/s - initial angular velocity) / t

Where the final angular velocity is 0 rad/s because the blade comes to a stop.

To find the number of revolutions the blade made before coming to a stop, we need to use the equation:

θ = ω_initial * t + 0.5 * α * t^2

where θ is the angular displacement.

Since the blade comes to a stop, the final angular displacement is 0, so the equation simplifies to:

0 = ω_initial * t + 0.5 * α * t^2

Now we can solve for the number of revolutions (n) made:

θ = ω_initial * t

n = θ / (2π radians)

Using these formulas, we can find the values.