(a) The angular displacement of the toy is 18.85 rad.
(b) The toy's angular velocity is 6.284 rad/min.
(c) if the counterclockwise rotation is in negative direction, the angular acceleration will be positive when the toy is turned off and vice versa.
The given parameters
The angular displacement of the toy is calculated as follows;
[tex]\theta = \frac{1 \ rev}{\min} \times 3\min \times \frac{2 \pi \ rad}{1 \ rev} = 18.85 \ rad[/tex]
[tex]\omega = \frac{1 \ rev}{\min} \times \frac{2 \pi \ rad}{1 \ rev} = 2\pi \ rad/\min = 6.284 \ rad/ \min[/tex]
let clockwise = positive direction
Let counterclockwise = negative direction
[tex]\alpha = \frac{\omega _f - \omega _i }{t}\\\\\alpha = \frac{0 - (-2\pi \ rad/\min)}{1 \min} = 2\pi\ rad/\min^2[/tex]
Thus, if the counterclockwise rotation is in negative direction, the angular acceleration will be positive when the toy is turned off and vice versa.
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