HW8: Rotational motion
Due: 11:59pm on Thursday, April 19, 2018
You will receive no credit for items you complete after the assignment is due. Grading Policy
Linear and Rotational Quantities Conceptual Question
A merry-go-round is rotating at constant angular speed. Two children are riding the merry-go-round: Ana is riding at point A
and Bobby is riding at point B.
Part A
Which child moves with greater magnitude of linear velocity?
Hint 1. Distinguishing between linear velocity and angular velocity
Ana’s (or Bobby’s) linear velocity is determined by the actual distance traveled (typically in meters) in a given time
interval. The angular velocity is determined by the angle through which (s)he rotates (typically in radians) in a
given time interval.
ANSWER:
Ana has the greater magnitude of linear velocity.
Bobby has the greater magnitude of linear velocity.
Both Ana and Bobby have the same magnitude of linear velocity.
Correct
The linear velocity is often just referred to as the velocity. The tangential velocity and radial velocity are
components of the linear velocity. In this scenario, since the merry-go-round has a constant angular velocity,
the radial velocity is zero, therefore the tangential velocity is equal to the linear velocity.
,Part B
Who moves with greater magnitude of angular velocity?
Hint 1. Distinguishing between velocity and angular velocity
Ana’s (or Bobby’s) velocity is determined by the actual distance she (he) travels (typically in meters) in a given
time interval. Her (His) angular velocity is determined by the angle through which she (he) rotates (typically in
radians) in a given time interval.
ANSWER:
Ana has the greater magnitude of angular velocity.
Bobby has the greater magnitude of angular velocity.
Both Ana and Bobby have the same magnitude of angular velocity.
Correct
Part C
Who moves with greater magnitude of tangential acceleration?
Hint 1. Distinguishing tangential, centripetal, and angular acceleration
Ana’s tangential and centripetal acceleration are components of her acceleration vector. During circular motion, if
Ana’s speed is changing (meaning the merry-go-round is speeding up or slowing down) she will have a nonzero
tangential acceleration. However, even if the merry-go-round is turning at constant angular speed, she will
experience a centripetal acceleration, because the direction of her velocity vector is changing (you can’t move
along a circular path unless your direction of travel is changing!).
Both tangential and centripetal accelerations have units of m/s2 , since they are the two-dimensional
components of linear acceleration. Angular acceleration, on the other hand, is a measure of the change in Ana’s
angular velocity. If her rate of rotation is changing, she will have a nonzero angular acceleration. Thus, angular
acceleration has units of rad/s2 .
ANSWER:
Ana has the greater magnitude of tangential acceleration.
Bobby has the greater magnitude of tangential acceleration.
Both Ana and Bobby have the same magnitude of tangential acceleration.
, Correct
Both Ana and Bobby are maintaining a constant speed, so they both have a tangential acceleration of zero
(thus they are equal)!
Part D
Who has the greater magnitude of centripetal acceleration?
Hint 1. Distinguishing tangential, centripetal, and angular acceleration
Ana’s tangential and centripetal acceleration are components of her acceleration vector. For circular motion, if
Ana’s speed is changing (meaning the merry-go-round is speeding up or slowing down) she will have a nonzero
tangential acceleration. However, even if the merry-go-round is turning at constant angular speed, she will
experience a centripetal acceleration, because the direction of her velocity vector is changing (you can’t move
along a circular path unless your direction of travel is changing!).
Both tangential and centripetal accelerations have units of m/s2 , since they are the two-dimensional
components of linear acceleration. Angular acceleration, on the other hand, is a measure of the change in Ana’s
angular velocity. If her rate of rotation is changing, she will have a nonzero angular acceleration. Thus, angular
acceleration has units of rad/s2 .
ANSWER:
Ana has the greater magnitude of centripetal acceleration.
Bobby has the greater magnitude of centripetal acceleration.
Both Ana and Bobby have the same magnitude of centripetal acceleration.
Correct
Part E
Who moves with greater magnitude of angular acceleration?
Hint 1. Distinguishing tangential, centripetal, and angular acceleration
Ana’s tangential and centripetal acceleration are components of her acceleration vector. For circular motion, if
Ana’s speed is changing (meaning the merry-go-round is speeding up or slowing down) she will have a nonzero
tangential acceleration. However, even if the merry-go-round is turning at constant angular speed, she will
experience a centripetal acceleration, because the direction of her velocity vector is changing (you can’t move
along a circular path unless your direction of travel is changing!).
Both tangential and centripetal accelerations have units of m/s2 , since they are the two-dimensional
components of linear acceleration. Angular acceleration, on the other hand, is a measure of the change in Ana’s
angular velocity. If her rate of rotation is changing, she will have a nonzero angular acceleration. Thus, angular
acceleration has units of rad/s2 .
, ANSWER:
Ana has the greater magnitude of angular acceleration.
Bobby has the greater magnitude of angular acceleration.
Both Ana and Bobby have the same magnitude of angular acceleration.
Correct
Both Ana and Bobby are maintaining a constant angular velocity, so they both have an angular acceleration of
zero (thus they are equal)!
Constant Angular Acceleration in the Kitchen
Dario, a prep cook at an Italian restaurant, spins a salad spinner and observes that it rotates 20.0 times in 5.00 seconds and
then stops spinning it. The salad spinner rotates 6.00 more times before it comes to rest. Assume that the spinner slows
down with constant angular acceleration.
Part A
What is the magnitude of the angular acceleration of the salad spinner as it slows down?
Express your answer numerically in radians per second per second.
Hint 1. How to approach the problem
Recall from your study of kinematics the three equations of motion derived for systems undergoing constant
linear acceleration. You are now studying systems undergoing constant angular acceleration and will need to
work with the three analogous equations of motion. Collect your known quantities and then determine which of
the angular kinematic equations is appropriate to find the angular acceleration α .
Hint 2. Find the angular velocity of the salad spinner while Dario is spinning it
What is the angular velocity of the salad spinner as Dario is spinning it?
Express your answer numerically in radians per second.
Hint 1. Converting rotations to radians
When the salad spinner spins through one revolution, it turns through 2π radians.
ANSWER:
ω0 = 25.1 radians/s
Hint 3. Find the angular distance the salad spinner travels as it comes to rest
Due: 11:59pm on Thursday, April 19, 2018
You will receive no credit for items you complete after the assignment is due. Grading Policy
Linear and Rotational Quantities Conceptual Question
A merry-go-round is rotating at constant angular speed. Two children are riding the merry-go-round: Ana is riding at point A
and Bobby is riding at point B.
Part A
Which child moves with greater magnitude of linear velocity?
Hint 1. Distinguishing between linear velocity and angular velocity
Ana’s (or Bobby’s) linear velocity is determined by the actual distance traveled (typically in meters) in a given time
interval. The angular velocity is determined by the angle through which (s)he rotates (typically in radians) in a
given time interval.
ANSWER:
Ana has the greater magnitude of linear velocity.
Bobby has the greater magnitude of linear velocity.
Both Ana and Bobby have the same magnitude of linear velocity.
Correct
The linear velocity is often just referred to as the velocity. The tangential velocity and radial velocity are
components of the linear velocity. In this scenario, since the merry-go-round has a constant angular velocity,
the radial velocity is zero, therefore the tangential velocity is equal to the linear velocity.
,Part B
Who moves with greater magnitude of angular velocity?
Hint 1. Distinguishing between velocity and angular velocity
Ana’s (or Bobby’s) velocity is determined by the actual distance she (he) travels (typically in meters) in a given
time interval. Her (His) angular velocity is determined by the angle through which she (he) rotates (typically in
radians) in a given time interval.
ANSWER:
Ana has the greater magnitude of angular velocity.
Bobby has the greater magnitude of angular velocity.
Both Ana and Bobby have the same magnitude of angular velocity.
Correct
Part C
Who moves with greater magnitude of tangential acceleration?
Hint 1. Distinguishing tangential, centripetal, and angular acceleration
Ana’s tangential and centripetal acceleration are components of her acceleration vector. During circular motion, if
Ana’s speed is changing (meaning the merry-go-round is speeding up or slowing down) she will have a nonzero
tangential acceleration. However, even if the merry-go-round is turning at constant angular speed, she will
experience a centripetal acceleration, because the direction of her velocity vector is changing (you can’t move
along a circular path unless your direction of travel is changing!).
Both tangential and centripetal accelerations have units of m/s2 , since they are the two-dimensional
components of linear acceleration. Angular acceleration, on the other hand, is a measure of the change in Ana’s
angular velocity. If her rate of rotation is changing, she will have a nonzero angular acceleration. Thus, angular
acceleration has units of rad/s2 .
ANSWER:
Ana has the greater magnitude of tangential acceleration.
Bobby has the greater magnitude of tangential acceleration.
Both Ana and Bobby have the same magnitude of tangential acceleration.
, Correct
Both Ana and Bobby are maintaining a constant speed, so they both have a tangential acceleration of zero
(thus they are equal)!
Part D
Who has the greater magnitude of centripetal acceleration?
Hint 1. Distinguishing tangential, centripetal, and angular acceleration
Ana’s tangential and centripetal acceleration are components of her acceleration vector. For circular motion, if
Ana’s speed is changing (meaning the merry-go-round is speeding up or slowing down) she will have a nonzero
tangential acceleration. However, even if the merry-go-round is turning at constant angular speed, she will
experience a centripetal acceleration, because the direction of her velocity vector is changing (you can’t move
along a circular path unless your direction of travel is changing!).
Both tangential and centripetal accelerations have units of m/s2 , since they are the two-dimensional
components of linear acceleration. Angular acceleration, on the other hand, is a measure of the change in Ana’s
angular velocity. If her rate of rotation is changing, she will have a nonzero angular acceleration. Thus, angular
acceleration has units of rad/s2 .
ANSWER:
Ana has the greater magnitude of centripetal acceleration.
Bobby has the greater magnitude of centripetal acceleration.
Both Ana and Bobby have the same magnitude of centripetal acceleration.
Correct
Part E
Who moves with greater magnitude of angular acceleration?
Hint 1. Distinguishing tangential, centripetal, and angular acceleration
Ana’s tangential and centripetal acceleration are components of her acceleration vector. For circular motion, if
Ana’s speed is changing (meaning the merry-go-round is speeding up or slowing down) she will have a nonzero
tangential acceleration. However, even if the merry-go-round is turning at constant angular speed, she will
experience a centripetal acceleration, because the direction of her velocity vector is changing (you can’t move
along a circular path unless your direction of travel is changing!).
Both tangential and centripetal accelerations have units of m/s2 , since they are the two-dimensional
components of linear acceleration. Angular acceleration, on the other hand, is a measure of the change in Ana’s
angular velocity. If her rate of rotation is changing, she will have a nonzero angular acceleration. Thus, angular
acceleration has units of rad/s2 .
, ANSWER:
Ana has the greater magnitude of angular acceleration.
Bobby has the greater magnitude of angular acceleration.
Both Ana and Bobby have the same magnitude of angular acceleration.
Correct
Both Ana and Bobby are maintaining a constant angular velocity, so they both have an angular acceleration of
zero (thus they are equal)!
Constant Angular Acceleration in the Kitchen
Dario, a prep cook at an Italian restaurant, spins a salad spinner and observes that it rotates 20.0 times in 5.00 seconds and
then stops spinning it. The salad spinner rotates 6.00 more times before it comes to rest. Assume that the spinner slows
down with constant angular acceleration.
Part A
What is the magnitude of the angular acceleration of the salad spinner as it slows down?
Express your answer numerically in radians per second per second.
Hint 1. How to approach the problem
Recall from your study of kinematics the three equations of motion derived for systems undergoing constant
linear acceleration. You are now studying systems undergoing constant angular acceleration and will need to
work with the three analogous equations of motion. Collect your known quantities and then determine which of
the angular kinematic equations is appropriate to find the angular acceleration α .
Hint 2. Find the angular velocity of the salad spinner while Dario is spinning it
What is the angular velocity of the salad spinner as Dario is spinning it?
Express your answer numerically in radians per second.
Hint 1. Converting rotations to radians
When the salad spinner spins through one revolution, it turns through 2π radians.
ANSWER:
ω0 = 25.1 radians/s
Hint 3. Find the angular distance the salad spinner travels as it comes to rest
