The angular velocity of a 755-g wheel 15.0 cm in diameter is given by the equation ω(t) = (2.00 rad/s2)t + (1.00 rad/s4)t 3. (a) Through how many radians does the wheel turn during the first 2.00 s of its motion? (b) What is the angular acceleration (in rad/s2) of the wheel at the end of the first 2.00 s of its motion?

a

The number of radians turned by the wheel in 2s is  

b

The angular acceleration is  

Explanation:

        The angular velocity  is given as

Now generally the integral of angular velocity gives angular displacement

           So integrating the equation of angular velocity through the limit 0 to 2 will gives us the angular displacement for 2 sec

    This is mathematically evaluated as

Now generally the derivative  of angular velocity gives angular acceleration

      So the value of the derivative of angular velocity equation at t= 2 gives us the angular acceleration

    This is mathematically evaluated as          

so at t=2

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