The crankshaft in a race car goes from rest to 3000 rpm in 3.0 s.

Part A: What is the angular acceleration of the crankshaft? Express your answer in radians per second squared.

Part B: How many revolutions does it make while reaching 3000 rpm? Express your answer in revolutions.

Question

High School

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Answer :

monikasaxena8519 monikasaxena8519 · Answer 1 · 2023-12-28T20:46:19-05:00

Part A: The angular acceleration of the crankshaft is (100π / 3) radians/second².

Part B: The crankshaft makes 50 revolutions while reaching 3000 rpm.

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.

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.

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