In general, is the sign of an object\'s average angular velocity the same as its
ID: 2151122 • Letter: I
Question
In general, is the sign of an object's average angular velocity the same as its initial angle ?0, its final angle ?, or the difference ? - ?0 between its final and initial angles?The sign of an object's average angular velocity is the same as its initial angle ?0.
The sign of an object's average angular velocity is the same as the difference ? - ?0
The sign of an object's average angular velocity is the same as its final angle ?.
Correct. The average angular velocity ? has the same sign as ? - ?0, because ? = according to Equation 8.2 (see ).
(b) The table that follows lists four pairs of initial and final angles of a wheel on a moving car. Decide which pairs give a positive average angular velocity and which give a negative average angular velocity.
Initial angle ?0 Final angle ?
(a) 0.35 rad 0.75 rad
(b) 0.94 rad 0.44 rad
(c) 6.2 rad 4.2 rad
(d) 3.0 rad 4.6 rad
Pairs (a) and (d) give a positive angular velocity and pairs (b) and (c) give a negative angular velocity.
Pair (a) gives a positive angular velocity and pairs (b), (c), and (d) give a negative angular velocity.
Pairs (a) and (c) give a positive angular velocity and pairs (b) and (d) give a negative angular velocity.
Pairs (a), (b), and (c) give a positive angular velocity and pair (d) gives a negative angular velocity.
Pairs (b) and (c) give a positive angular velocity and pairs (a) and (d) give a negative angular velocity.
Correct. The direction of the car's average angular velocity is the same as its angular displacement (see ). The angular displacement is the difference ? - ?0 between the final angle ? and the initial angle ?0. In (a) and (d), this difference is positive, while in (b) and (c) it is negative.
The elapsed time for each pair of angles is 2.1 s.
(c) What is the algebraic expression for the average angular velocity ? of an object? Express your answer in terms of the object's initial angle and time (?0 and t0), and the final angle and time (? and t). (Answer using theta_0 to be the initial angle, t_0 to be the initial time, theta to be the final angle, and t to be the final time).
? =
(d) Determine the magnitude and direction of the average angular velocity ? for the data in the first row of the table. Include an explicit plus or minus sign along with your numerical answer to denote the direction.
Sign Number Unit
? =
Your response differs from the correct answer by more than 100%.
(e) Determine the magnitude and direction of the average angular velocity ? for the data in the second row of the table. Include an explicit plus or minus sign along with your numerical answer to denote the direction.
Sign Number Unit
? =
Your response differs from the correct answer by more than 100%.
(f) Determine the magnitude and direction of the average angular velocity ? for the data in the third row of the table. Include an explicit plus or minus sign along with your numerical answer to denote the direction.
Sign Number Unit
? =
Your response differs from the correct answer by more than 100%.
(g) Determine the magnitude and direction of the average angular velocity ? for the data in the fourth row of the table. Include an explicit plus or minus sign along with your numerical answer to denote the direction.
Sign Number Unit
? =
Your response differs from the correct answer by more than 100%.
Explanation / Answer
The sign of an object's average angular velocity is the same as the difference ? - ?0 Pairs (a) and (c) give a positive angular velocity and pairs (b) and (d) give a negative angular velocity.