A solid body rotates with angular velocity vecomega=3thati+2t^(2) hatj rad//s . Find (a) the magnitude of angular velocity and angular acceleration at time t=1 s and (b) the angle between the vectors of the angular velocity and the angular acceleration at that moment.
A particle rotates in a circle with angular speed omega_(0) . A retarding force decelerates it such that angular deceleration is always proportional to square root of angular velocity. Find the mean angular velocity of the particle averaged over the whole time of rotation.
A solid body rotates with deceleration about a stationary axis with an angular deceleration betapropsqrt(omega) , where omega is its angular velocity. Find the mean angular velocity of the body averaged over the whole time of rotation if at the initial moment of time its angular velocity was equal to omega_0 .
In nonuniform circular motion, the linear acceleration vec a , the angular acceleration, vec alpha , the angular velocity vec v the radius vector vec r and the angular velocity vec omega at any instant are related by the vector equation,
A particle is moving in a circular orbit of radius r_(1) with an angular velocity omega_(1) It jumps to another circular orbit of radius r_(2) and attains an angular velocity omega_(2) . If r_(2)= 0.5 r_(1) , and if no external torque is applied to the system, then the new angular velocity omega_(2) is given by
A flywheel with the initial angular velocity omega_0 decelerates due to the forces whose moment relative to the axis is proportional to the square root of its angular velocity. Find the mean angular velocity of the flywheel averaged over the total decleration time.
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