A) A ladybug sits at the edge of a turntable of radius 30 cm. The turntable spin
ID: 1785194 • Letter: A
Question
A) A ladybug sits at the edge of a turntable of radius 30 cm. The turntable spins at a steady rate of 1 revolution every 4 seconds. What is the angular speed of the ladybug?
Hint: what is (in radians!) for one revolution?
B) A ladybug sits at the edge of a turntable of radius 30 cm. The turntable spins at a steady rate of 1 revolution every 4 seconds. What is the linear speed (also known as tangential speed) of the ladybug?
Hint: what distance does the ladybug travel in one revolution?
C) A ladybug sits at the outer edge of a merry-go-round, and a gentleman bug sits halfway between her and the axis of rotation. The merry-go-round makes a complete revolution once each second. The gentleman bug’s angular speed is
D) A ladybug sits at the outer edge of a merry-go-round, and a gentleman bug sits halfway between her and the axis of rotation. The merry-go-round makes a complete revolution once each second. The gentleman bug’s linear speed (also known as tangential speed) is
E)
For rotational motion, we will use the convention that positive angular velocity means the object (often a disk) is spinning in a counterclockwise direction and negative angular velocity means the object is spinning in a clockwise direction. This is akin to linear motion where positive velocity means the object is moving to the right and negative velocity means the object is moving to the left. This connection can be very useful when conceptualizing rotational motion.
Suppose a disk is spinning counterclockwise and slowing down. Which of the following are correct regarding the signs of angular velocity and angular acceleration? (Thinking about linear velocity and linear acceleration for an object moving to the right and slowing down should help!)
Angular velocity < 0, angular acceleration < 0
Angular velocity < 0, angular acceleration > 0
Angular velocity > 0, angular acceleration < 0
Angular velocity > 0, angular acceleration > 0
F)
For rotational motion, we will use the convention that positive angular velocity means the object (often a disk) is spinning in a counterclockwise direction and negative angular velocity means the object is spinning in a clockwise direction. This is akin to linear motion where positive velocity means the object is moving to the right and negative velocity means the object is moving to the left. This connection can be very useful when conceptualizing rotational motion.
Suppose a disk is spinning clockwise and speeding up. Which of the following are correct regarding the signs of angular velocity and angular acceleration? (Thinking about linear velocity and linear acceleration for an object moving to the left and slowing down should help!)
Angular velocity < 0, angular acceleration < 0
Angular velocity < 0, angular acceleration > 0
Angular velocity > 0, angular acceleration < 0
Angular velocity > 0, angular acceleration > 0
Angular velocity < 0, angular acceleration < 0
Angular velocity < 0, angular acceleration > 0
Angular velocity > 0, angular acceleration < 0
Angular velocity > 0, angular acceleration > 0
F)
For rotational motion, we will use the convention that positive angular velocity means the object (often a disk) is spinning in a counterclockwise direction and negative angular velocity means the object is spinning in a clockwise direction. This is akin to linear motion where positive velocity means the object is moving to the right and negative velocity means the object is moving to the left. This connection can be very useful when conceptualizing rotational motion.
Suppose a disk is spinning clockwise and speeding up. Which of the following are correct regarding the signs of angular velocity and angular acceleration? (Thinking about linear velocity and linear acceleration for an object moving to the left and slowing down should help!)
Angular velocity < 0, angular acceleration < 0
Angular velocity < 0, angular acceleration > 0
Angular velocity > 0, angular acceleration < 0
Angular velocity > 0, angular acceleration > 0
Explanation / Answer
(1) We know that the rotation in rad in 1 revolution = 2Pi
hence the angular speed = 2Pi /T = 2Pi/ 4 = 1.571 rad /s
(2) we know that the linear speed (v) = wR
where R is the distance from the axis = 1.571*(0.3) = 0.471 m/s
(3) Here time period is 1 sec
angular speed (w) = 2Pi / 1= 6.283 rad/s
(4) Gentleman's bug distance = 30/2 = 15 cm = 0.15 m
Hence the linear or tangential speed = wR = 6.283*0.15 = 0.9424 m/s
(5) Since the disk is spinning in the counterclockwise direction therefore the angular velocity must be negative.
hence it will be less than ZERO.
Simultaneoulsy it is slowing down that means the angular acceleration provided to the disk is in clockwise direction so that would be positive.
Hence it would be greater than ZERO.
So correct option is b .
(6) Since disk is moving in clockwise direction
so angular velocity must be positive.
Also speeding up therefore angular acceleration would be positive.
Hence correct option would be d.
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