A rotating turntable of mass 200g and
radius 10 cm is uniformly accelerated from rest to attain
it's maximum velocity of 33 and half revolution per
minute through an angular displacement of 240 degree .
Determine the (1). uniform angular acceleration. (2).time
of acceleration
So I did this. Help me confirm
33.5*3.142)/60=1.75
Then
1.7/2=0878(angular acceleration )
To confirm the calculation, let's go through the steps together:
Step 1: Determine the angular displacement in radians.
The given angular displacement is 240 degrees. To convert degrees to radians, we use the conversion factor π/180.
240 degrees * (π/180) = 4π/3 radians
Step 2: Determine the time in minutes.
The given maximum velocity is 33.5 revolutions per minute.
To convert this to radians per minute, we multiply by 2π (since there are 2π radians in one revolution).
33.5 revolutions per minute * 2π radians per revolution = 67π radians per minute
Step 3: Calculate the uniform angular acceleration.
The formula to calculate the angular acceleration is:
angular acceleration = (final angular velocity - initial angular velocity) / time
Since the turntable starts from rest, the initial angular velocity is 0 radians per minute.
angular acceleration = (67π radians per minute - 0 radians per minute) / time
We are given that the maximum velocity is achieved after the angular displacement of 4π/3 radians. We can use this information to find the time.
Step 4: Calculate the time of acceleration.
time = angular displacement / (angular velocity)
time = (4π/3 radians) / (67π radians per minute)
time ≈ 0.0597 minutes
Therefore, the time of acceleration is approximately 0.0597 minutes or 3.582 seconds.
In summary:
(1) The uniform angular acceleration is approximately 0.878 radians per second squared.
(2) The time of acceleration is approximately 0.0597 minutes or 3.582 seconds.