## Angular Acceleration and Revolutions

**The crankshaft in a race car goes from rest to 3500 rpm in 3.5 seconds.**

**What is the crankshaft’s angular acceleration?**

Known Variables:

time: 3.5 seconds

angular frequency(ω): 3500 rpm

We know that the **angular acceleration** formula is as follows:

**α**= ω/t

First we need to convert ω into proper units which is in radians/second.

3500 rpm x 2π/60 = 366.52 rad/s^{2}

since we found ω, we can now solve for the angular acceleration (γ= ω/t).

**α**= 366.52/ 3.5

= 104 **rad/s**^{2}

or in two significant figures, 100 **rad/s**^{2}

**α= **100 **rad/s ^{2}**

**How many revolutions does it make while reaching 3500 rpm?**

First is to find the total angular displacement during the acceleration:

**angular displacement (θ) **= (1/2)αt^{2}

=1/2 x ( 104 rad/s^{2} *(3.5s)^{2 })

θ = 637 rad

**number of Revolutions (n) **= θ/2π

= 637 rad/2π = 100 revs

**n=** 100 revolutions

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