Answer :
Part A: The angular acceleration of the crankshaft is (100π / 3) radians/second².
Part B: The crankshaft makes 50 revolutions while reaching 3000 rpm.
Part A:
To find the angular acceleration of the crankshaft, we can use the formula:
angular acceleration (α) = (final angular velocity - initial angular velocity) / time
First, let's convert the final angular velocity of 3000 rpm to radians per second:
final angular velocity = 3000 rpm * (2π radians / 1 minute) * (1 minute / 60 seconds)
= 3000 * 2π / 60 radians/second
= 100π radians/second
The initial angular velocity is 0 since the crankshaft starts from rest.
Plugging in the values into the formula:
angular acceleration = (100π radians/second - 0 radians/second) / 3.0 seconds
= (100π / 3) radians/second²
So the angular acceleration of the crankshaft is (100π / 3) radians/second².
Part B:
To find the number of revolutions the crankshaft makes while reaching 3000 rpm, we can use the formula:
number of revolutions = (final angular velocity - initial angular velocity) / (2π)
Plugging in the values:
number of revolutions = (100π radians/second - 0 radians/second) / (2π)
= 50 revolutions
Therefore, the crankshaft makes 50 revolutions while reaching 3000 rpm.
To know more about angular acceleration
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