A wheel has a constant angular acceleration of 3 rad/s^2. In a 4 second interval it turns through an angle of 120 radians. Assuming the wheel started from rest, how long had it been in motion from the start of thus 4 second interval?

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Answer 1 · 2018-06-09T12:24:29

The time is #=8s#

The angular acceleration is #alpha=3rads^-2#

The angle is #theta=120rad#

The time is #t=4s#

Apply the equation,

#theta=omega_1t+1/2alphat^2#

#120=4omega_1+1/2*3*16=4omega+24#

#omega_1=(120-24)/4=24rads^-1#

The initial angular velocity is #omega_0=0rads^-1#

Apply the equation

#omega_1=omega_0+alphat_1#

#24=0+3t_1#

#3t_1=24#

#t_1=24/3=8s#