A high-speed drill rotating ccw at 2300 rpm comes to a halt in 2.9 s .
you do not say what the question is
average rpm during stop = 1150
turns to stop = 1150 *2.9/60
original radians/s
= 2300 revs/min*2 pi rad/rev *1min/60 s
= 241 radians/s
angular acceleration = -241/2.9
whatever
To find the angular acceleration of the drill, we can use the formula:
angular acceleration (α) = (final angular velocity - initial angular velocity) / time
Given:
Initial angular velocity (ω₁) = 2300 rpm (rotation per minute)
Final angular velocity (ω₂) = 0 (since the drill comes to a halt)
Time (t) = 2.9 s
Since the initial angular velocity is given in rpm, we need to convert it to radians per second (rad/s). We know that one revolution is equivalent to 2π radians. Therefore:
Initial angular velocity (ω₁) = 2300 rpm * (2π rad/1 min) * (1 min/60 s)
ω₁ = 2300 * 2π / 60 rad/s ≈ 240.68 rad/s
Now we can calculate the angular acceleration:
α = (ω₂ - ω₁) / t
α = (0 - 240.68) / 2.9 rad/s²
α ≈ -83.23 rad/s²
Therefore, the angular acceleration of the drill is approximately -83.23 rad/s². The negative sign indicates that the drill is decelerating (slowing down) in the counterclockwise direction.
To calculate the angular acceleration of the high-speed drill, we can use the formula:
Angular acceleration (α) = Change in angular velocity (Δω) / Time taken (Δt)
Given:
Initial angular velocity (ω0) = 2300 rpm (rotations per minute)
Final angular velocity (ωf) = 0 rpm (since the drill comes to a halt)
Time taken (Δt) = 2.9 s
Step 1: Convert the initial and final angular velocity to radians per second.
We know that there are 2π radians in one revolution (360 degrees) and 60 seconds in one minute.
Initial angular velocity (ω0) = 2300 rpm
= 2300 rotations / 1 minute
= (2300 rotations / 1 minute) * (2π radians / 1 rotation) * (1 minute / 60 seconds)
= (2300 * 2π) / 60 radians/second
Final angular velocity (ωf) = 0 rpm
= 0 rotations / 1 minute
= 0 radians/second
Step 2: Calculate the change in angular velocity (Δω)
Δω = ωf - ω0
Δω = 0 - (2300 * 2π) / 60 radians/second
Step 3: Calculate the angular acceleration (α)
α = Δω / Δt
α = [0 - (2300 * 2π) / 60] radians/second / 2.9 seconds
Now, you can substitute the values and calculate the angular acceleration.