A grindstone of radius 4.0m is initially spinning with an angular speed of 8.0 rad/s. The angular speed is then increased to 12 rad/s over 4.0s. Assume that the angular acceleration is constant. What is the average angular speed of grindstone?
To find the average angular speed of the grindstone, we need to calculate the total change in angular speed and divide it by the total time elapsed.
The initial angular speed is given as 8.0 rad/s, and the final angular speed is 12 rad/s. The time taken to go from the initial angular speed to the final angular speed is given as 4.0 seconds.
To calculate the average angular speed, we use the formula:
Average angular speed = (change in angular speed) / (time elapsed)
The change in angular speed is calculated by subtracting the initial angular speed from the final angular speed:
Change in angular speed = (final angular speed) - (initial angular speed)
= 12 rad/s - 8.0 rad/s
= 4.0 rad/s
The time elapsed is given as 4.0 seconds.
Now, we can calculate the average angular speed:
Average angular speed = (change in angular speed) / (time elapsed)
= 4.0 rad/s / 4.0 s
= 1.0 rad/s
Therefore, the average angular speed of the grindstone is 1.0 rad/s.
To find the average angular speed of the grindstone, we need to consider the initial and final angular speeds, as well as the time interval.
Given:
Initial angular speed (ω₁) = 8.0 rad/s
Final angular speed (ω₂) = 12 rad/s
Time interval (t) = 4.0 s
The average angular speed (ω_avg) can be calculated using the formula:
ω_avg = (ω₁ + ω₂) / 2
Substituting the given values:
ω_avg = (8.0 rad/s + 12 rad/s) / 2
= 20 rad/s / 2
= 10 rad/s
Therefore, the average angular speed of the grindstone is 10 rad/s.
You have to be kidding.
avg speed= (final+initial)/2