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Answer :
The crankshaft in a race car goes from rest to 3000 rpm in 2.0seconds.
1)157 rad/s² is the crankshafts angular acceleration
2) 50 revolutions need does it does it make in 3000rpm
The angular acceleration of the crankshaft can be calculated using the formula: angular acceleration (α) = (final angular velocity - initial angular velocity) / time. Given that the initial angular velocity is 0 and the final angular velocity is 3000 rpm (which needs to be converted to radians per second), the angular acceleration can be determined.
To calculate the number of revolutions made by the crankshaft in 3000 rpm, we can use the formula: number of revolutions = angular velocity / (2π), where the angular velocity needs to be converted from rpm to radians per second.
1. The initial angular velocity is 0 rpm, and the final angular velocity is 3000 rpm. To calculate the angular acceleration, we need to convert the final angular velocity to radians per second. Since 1 rpm is equal to 2π/60 radians per second, the final angular velocity is (3000 rpm) ×(2π/60) = 100π radians per second. The time taken is given as 2.0 seconds. Therefore, the angular acceleration is (100π radians per second - 0 radians per second) / 2.0 seconds = 50π radians per second squared.
2. To find the number of revolutions made in 3000 rpm, we use the formula: number of revolutions = angular velocity / (2π). The angular velocity in radians per second is (3000 rpm) × (2π/60) = 100π radians per second. Plugging this value into the formula, we get the number of revolutions = (100π radians per second) / (2π) = 50 revolutions. Thus, the crankshaft makes 50 revolutions in 3000 rpm.
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