A wheel rotating at 490 rev/min accelerates uniformly at 0.5 rad/s^2 for 30s. Find a. The angular velocity after 30s b. The pulleys peripheral speed if its diameter is 20cm c. The angle turned by the wheel during this time?

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Answer 1 · 2018-06-09T13:21:01

Please see the explanation below

The initial angular velocity is

#omega_0=490*2*pi/60=51.31rads^-1#

The angular acceleration is #alpha=0.5rads^-2#

The time is #t=30s#

Apply the equation

#omega=omega_0+alphat#

#omega=51.31+0.5*30=66.31rads^-1#

The angular velocity is #omega=66.31rads^-1# after #30s#

The diameter is #d=0.2m#

The radius is #r=0.1m#

The peripheral speed is

#v=omegar=66.31*0.1=6.63ms^-1#

The angle turned is

#theta=omega_0t+1/2alphat^2#

#=51.31*30+1/2*0.5*30^2#

#=1764.3rad#