How can object rotating counterclockwise have a positive angular acceleration? no se Now choose from one of the following options Why? a The counterclockwise rotation of an object produces negative angular velocity. Therefore, when the object is speeding up and rotating counterclockwise, the angular acceleration is positive. b The counterclockwise rotation of an object produces negative angular velocity. Therefore, when the object is slowing down and rotating counterclockwise, the angular acceleration is positive. c The counterclockwise rotation of an object produces positive angular velocity. Therefore, when the object is speeding up and rotating counterclockwise, the angular acceleration is positive. d The counterclockwise rotation of an object produces positive angular velocity. Therefore, when the object is slowing down and rotating counterclockwise, the angular acceleration is positive.
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An object has negative angular velocity ω and positive angular acceleration α. Which of the following is true about the object: it is rotating clockwise, speeding up it is rotating counterclockwise, speeding up it is rotating counterclockwise, slowing down it is rotating clockwise, slowing down
Dwijendra R.
The kinematic equations for rotational motion are valid for constant angular acceleration, changing angular acceleration, constant angular velocity, and changing angular velocity. By convention, a torque which has a tendency to cause a counter-clockwise rotation is said to be positive, while a torque which has a tendency to cause a clockwise rotation is said to be negative. The equation Iω best describes the angular momentum for a rotating object about a fixed axis. If the angular acceleration is nonzero and constant, the object must be steadily increasing or decreasing its angular velocity. For an object to be in rotational equilibrium, the net torque must be equal to zero. If a constant net torque is applied to an object with a fixed axis, the object will experience a constant angular acceleration resulting in a changing angular velocity.
Jeff V.
(a) In general, does the average angular acceleration of a rotating object have the same direction as its initial angular velocity $\omega_{0}$, its final angular velocity $\omega,$ or the difference $\omega-\omega_{0}$ between its final and initial angular velocities? (b) The table that follows lists four pairs of initial and final angular velocities for a rotating fan blade. Determine the direction (positive or negative) of the average angular acceleration for each pair. Provide reasons for your answers. $$ \begin{array}{|c|c|c|} \hline & \text { Initial angular velocity } \omega_{0} & \text { Final angular velocity } \omega \\ \hline \text { (a) } & +2.0 \mathrm{rad} / \mathrm{s} & +5.0 \mathrm{rad} / \mathrm{s} \\ \hline \text { (b) } & +5.0 \mathrm{rad} / \mathrm{s} & +2.0 \mathrm{rad} / \mathrm{s} \\ \hline \text { (c) } & -7.0 \mathrm{rad} / \mathrm{s} & -3.0 \mathrm{rad} / \mathrm{s} \\ \hline \text { (d) } & +4.0 \mathrm{rad} / \mathrm{s} & -4.0 \mathrm{rad} / \mathrm{s} \\ \hline \end{array} $$ Problem The elapsed time for each of the four pairs of angular velocities is $4.0 \mathrm{~s}$. Find the average angular acceleration (magnitude and direction) for each of the four pairs. Be sure that your directions agree with those found in the Concept Question.
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