A rigid body is rotating counterclockwise about a fixed axis. Each of the following pairs of quantities represents an initial angular position and a final angular position of the rigid body. Which of the sets can occur only if the rigid body rotates through more than 180°? (a) 3 rad, 6 rad; (b) –1 rad, 1 rad; (c) 1 rad, 5 rad.
A rigid body is rotating counterclockwise about a fixed axis. Each of the following pairs of quantities represents an initial angular position and a final angular position of the rigid body. Which of the sets can occur only if the rigid body rotates through more than 180°? (a) 3 rad, 6 rad; (b) –1 rad, 1 rad; (c) 1 rad, 5 rad.
(a)
The angular position initially is: ωi = 3 rad
The final angular position is ωf = 6 rad.
The rotation of the body is given as:
Δ θ > 180°
Δ θ > 3.14 rad
The expression of the angular rotation is given as:
Substitute the value in the above equation.
Thus, the angular position of the rigid body is 3 rad.
(b)
The body angular position initially is: ωi = -1 rad
The body's final angular position is ωf = 1 rad.
The rotation of the body is given as:
Δ θ > 180°
Δ θ > 3.14 rad
The expression of the angular rotation is given as:
Substitute the value in the above equation.
Thus, the angular position of the rigid body is 2 rad.
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