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Angular Impulse From Variable Torque

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A torque is applied to a wheel that is initially at rest. The torque varies with time $t$ according to the function τ(t)=(2.0 N⋅m/s2)t2−(0.5 N⋅m/s)t\tau(t) = (2.0\ \mathrm{N \cdot m/s^2})t^2 - (0.5\ \mathrm{N \cdot m / s})t. What is the angular impulse on the wheel during the time interval from $t=0$ to $t=4.0\ \mathrm{s}$?

A

24.00 N·m·s

B

42.67 N·m·s

C

32.00 N·m·s

D

38.67 N·m·s

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