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The crankshaft (radius = 3 cm) in a race car accelerates uniformly from rest to 3000 rpm in 2.0 seconds. How many revolutions does it make while reaching 3000 rpm?

Answer :

Using Angular Acceleration of the crankshaft, It makes 50 revolutions while reaching 3000 rpm.

The temporal rate at which angular velocity changes is known as angular acceleration. The standard unit of measurement is radians per second per second. Therefore, = d d t. Rotational acceleration is another name for angular acceleration.

u = 0 for the initial angular velocity

Final v = 3000 rpm, which is 3000 2/60 rad/s, equals 314 rad/s.

clock, t = 2.0 s

a. The first equation of rotational motion gives the angular acceleration:

The formula is: = (v-u)/t = (314 rad/s-0)/2.0 s = 157 rad/s2.

b. the quantity of rotations completed before attaining the 3000 rpm final angular velocity. Time spent: 2 seconds.

Use the second rotational motion equation:

θ = u t + 0.5 α t²

⇒ θ = 0 + 0.5 × 157 rad/s² × (2.0 s.) (2.0 s.)

= 314 rad

The number of revolutions, n, is equal to θ / 2π = 314/ 2π = 50 revolutions.

To learn more about Angular acceleration from given link

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