A wind turbine is rotating counterclockwise at 0.78 rev/s and slows to a stop in 21 s. Its blades are 27 m in length.

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Chapter1: Units, Trigonometry. And Vectors
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**Wind Turbine Rotational Problem**

A wind turbine is rotating counterclockwise at 0.78 revolutions per second and slows to a stop in 21 seconds. Its blades are 27 meters in length.

**(a)** What is the angular acceleration of the turbine (in \(\text{rad/s}^2\))? (Indicate the direction with the sign of your answer.)

\[ \boxed{\phantom{0}} \, \text{rad/s}^2 \]

**(b)** What is the centripetal acceleration (in \(\text{m/s}^2\)) of the tip of the blades at \(t = 0\)? (Enter the magnitude. Round your answer to at least two decimal places.)

\[ \boxed{\phantom{0}} \, \text{m/s}^2 \]

**(c)** What is the magnitude (in \(\text{m/s}^2\)) of the total linear acceleration of the tip of the blades at \(t = 0\)? (Round your answer to at least two decimal places.)

\[ \boxed{\phantom{0}} \, \text{m/s}^2 \]

What is the angle that this total linear acceleration vector makes with the centripetal acceleration vector? (Enter the magnitude of the smallest such angle in degrees.)

\[ \boxed{\phantom{0}} \, ^\circ \]
Transcribed Image Text:**Wind Turbine Rotational Problem** A wind turbine is rotating counterclockwise at 0.78 revolutions per second and slows to a stop in 21 seconds. Its blades are 27 meters in length. **(a)** What is the angular acceleration of the turbine (in \(\text{rad/s}^2\))? (Indicate the direction with the sign of your answer.) \[ \boxed{\phantom{0}} \, \text{rad/s}^2 \] **(b)** What is the centripetal acceleration (in \(\text{m/s}^2\)) of the tip of the blades at \(t = 0\)? (Enter the magnitude. Round your answer to at least two decimal places.) \[ \boxed{\phantom{0}} \, \text{m/s}^2 \] **(c)** What is the magnitude (in \(\text{m/s}^2\)) of the total linear acceleration of the tip of the blades at \(t = 0\)? (Round your answer to at least two decimal places.) \[ \boxed{\phantom{0}} \, \text{m/s}^2 \] What is the angle that this total linear acceleration vector makes with the centripetal acceleration vector? (Enter the magnitude of the smallest such angle in degrees.) \[ \boxed{\phantom{0}} \, ^\circ \]
A circular disk of radius 19 cm has a constant angular acceleration of 4.0 rad/s²; at t = 0 its angular velocity is 5.5 rad/s. (Enter the magnitudes.)

(a) Determine the disk's angular velocity (in rad/s) at t = 5.0 s.

[  ] rad/s

(b) What is the angle (in rad) it has rotated through during this time?

[  ] rad

(c) What is the tangential acceleration (in m/s²) of a point on the disk at t = 5.0 s?

[  ] m/s²
Transcribed Image Text:A circular disk of radius 19 cm has a constant angular acceleration of 4.0 rad/s²; at t = 0 its angular velocity is 5.5 rad/s. (Enter the magnitudes.) (a) Determine the disk's angular velocity (in rad/s) at t = 5.0 s. [ ] rad/s (b) What is the angle (in rad) it has rotated through during this time? [ ] rad (c) What is the tangential acceleration (in m/s²) of a point on the disk at t = 5.0 s? [ ] m/s²
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