Reading Assignment 2, Chapter 2
In order for an object to be in equilibrium the net torque on it must be N m.
0
The force of gravity is attractive, which makes the lever arm distance zero. Thus, the net torque on a planet due to the sun's gravity is
0
The plot depicts the position versus time of a toy car in one dimension. During which time interval(s) is the car stationary?
0--2 seconds 6--8 seconds
A car is traveling at a velocity of 40 m/s. The car then starts to accelerate at --5 m/s2. If the car accelerates for 6 seconds, it loses m/s.
30
Rank the following situations in order from the largest torque (top) to the smallest (bottom). The point of contact of the force is the same in all four cases.
DBAC
Angular momentum is directly proportional to which of the following?
Rotational inertia. Angular velocity.
The quantity that describes how fast an object is rotating through some angle is velocity.
angular
Two children of different weights are trying to balance a teeter-totter on a playground. The larger child needs to sit to the fulcrum than the smaller child in order to balance the teeter-totter.
closer
A torque is the rotational version of a
force
The torque on an object is the applied to the object times the lever arm.
force
The point in which the weight of the object exerts no torque is called the center of
gravity
The moment of inertia of an object depends on the
mass of the object distance from pivot
The perpendicular distance from the axis of rotation to the line of action of the applied force is called the
moment arm lever arm
The net torque, τnet, is proportional to the _____.
moment of inertia rotational acceleration
Which of the following would be units for angular acceleration?
rad/s2 rpm/s
Which of the following are units of rotational velocity?
radians per second RPM Hertz
When a moving bicycle starts to tip over
the rotational momentum of the tipping adds to the rotational momentum of the bicycle.
A figure skater starts to spin with arms extended, then pulls their arms in. Doing this ______.
their rotational momentum remains constant increases their rotational velocity decreases their moment of inertia
Which of the following are rotational displacements?
three revolutions thirty-five degrees four radians
True or False: If an object has some rotational acceleration, it must also have linear acceleration.
true
True or false: A child sitting on a merry-go-round doubles her distance from the center of rotation. At her new location, her linear speed is twice what it was prior to moving.
true
Which of the following are rotational velocities?
two and a half radians per second fifteen degrees per second two revolutions per minute
A person sitting closer to the center of rotation travels with a smaller linear compared with a person sitting farther away.
velocity
The change in the rotational displacement in a given time interval is called the rotational
velocity
The change in the rotational displacement in a given time interval is called the rotational .
velocity
The rotational momentum of an object is the moment of inertia times the rotational .
velocity
The ω symbol is commonly used to represent the rotational , while the θ symbol is commonly used for the rotational .
velocity displacement
The direction of positive torque is arbitrary. For this question, we will use counterclockwise as the direction in which the torque must cause the change in rotation in order for it to be positive; otherwise, the torque is negative. Which of the forces in the picture will produce a negative torque about the fulcrum?
C D F
Four equally massive boxes are affixed to massless rods able to rotate about the center circle as shown in the illustration. The boxes are not connected to one another, but each box has the same mass. Rank the boxes from the largest moment of inertia (top) to the smallest (bottom).
DABC
Two people are riding a merry-go-round, but one is sitting at the edge while the other is sitting half way between the edge and the center of the merry-go-round. Which quantities are smaller for the person on away from the edge?
Distance traveled. Linear velocity.
Two people are riding a merry-go-round, but one is sitting at the edge while the other is sitting half way between the edge and the center of the merry-go-round. Which quantities are smaller for the person on away from the edge?.
Distance traveled. Linear velocity.
Rank the following graphs (identified by letter) of velocity versus time with the largest positive acceleration at the top to the largest negative acceleration at the bottom.
E A C D B F
The sun with a counterclockwise orbiting planet is shown in the illustration. Match the directions with the different vectors.
Force of gravity on the planet by the sun=downward Velocity of the planet=leftwards lever arm distance=none
When you look at the face of an analog watch (one with hands rotating around the face) the direction of the angular velocity vector of the quick moving second hand is in which direction.
From the face of the clock away from your face.
Two people are riding a merry-go-round, but one is sitting at the edge while the other is sitting half way between the edge and the center of the merry-go-round. Which quantities are the same for both of them?
Rotational displacement. Time to complete one revolution. Rotational velocity.
Which of the following definitions applies to either rotational or linear accelerations?
The rate of change of the velocity. The rate of change of the rotational velocity.
If you wanted to double the linear speed of a child on a merry-go-round, which of the following could you double to accomplish this?
The rotational velocity. The distance from the center.
A wheel initially rotating at 2 revolutions per second is slowed down to rotate at only 1 revolution per second. During the slowdown the wheel's rotational velocity changed, which means it had rotational as well as rotational velocity.
acceleration
The net torque is proportional to the rotational . The proportionality constant is the moment of inertia.
acceleration
Rotational displacement is the quantity that tells what an object has rotated through.
angle
The angle that something rotates during its motion is called its rotational . It is often measured in either degrees, revolutions or radians.
displacement or distance
A child sitting on a merry-go-round has her father double the rotational velocity. At her new rotational velocity, her linear speed is what it was prior to being sped up.
double
If we consider the moment of inertia of some object then doubling the mass will the moment of inertia, but doubling the distance from the axis of rotation will the moment of inertia.
double quadruple
The equations for rotational motion can be obtained by looking at the equations for motion and substituting quantities for linear ones.
linear rotational
The moment of inertia, I, of a concentrated mass (the object) at the end of a very light rod depends on the object's _____.
mass distance from the axis of rotation, squared
the net torque, τnet, is proportional to the _____.
moment of inertia rotational acceleration
A person holding weights, out away from their body, slowly spins on a rotating chair with negligible friction from the bearings. When they bring their arms in, the chair speeds up and spins faster. This occurs because the total rotational must remain constant.
momentum
The product of the rotational velocity with the moment of inertia is the rotational
momentum
The lever arm is the distance from the axis of rotation to the line of action of the applied force.
perpendicular
For the simple relationship between linear velocity and rotational velocity, v = rω, in which of the following units could the rotational velocity be expressed?
radians/hour radians/seconds
The radian is defined as the ratio of the arc length to the of the circle.
radius
The of an object to changing its state of rotational motion is called an object's rotational inertia.
resistance
Choose which of the following are units of rotational displacement
revolutions degrees radians
Choose which of the following are units of rotational displacement.
revolutions degrees radians
The center of gravity is a point in which if you put a fulcrum, the weight of the object will give zero . [insert one word in the blank]
torque
The moment of inertia times the rotational acceleration is equal to the net , just like the mass of an object times the acceleration is equal to the net force.
torque
Match the term of the velocity formula and the complete formula with its interpretation. Assume the object is undergoing constant acceleration.
v0 + at=The total velocity at any time. V0=The original velocity of the object when the motion started. at=The velocity that is gained or lost due to acceleration.
A student holds a spinning wheel horizontally such that the rotational momentum of the wheel is 1 kg m2/s. When the student flips the wheel, so that the rotational momentum of the wheel now points downwards, the rotational momentum of the student is _____.
2 kg m2/s upwards
A runner traveling at 5 m/s begins to accelerate at 1 m/s2 for 4 seconds. Without the acceleration, the runner would have ran only m during those 4 seconds; however, the acceleration added an extra m.
20 8
A heavy mass is held fixed on a rigid rod of negligible mass. The moment of inertia of the mass and rod is found to be 12 kg m2. The heavy mass is then moved closer to the axis of rotation along the rod, so that it is now half as far from the axis of rotation then it was. The moment of inertia of the rod is now kg m2.
3
The velocity versus time of a toy car is plotted in the adjoining graph. Rank the distance traveled by the car from largest (top) to smallest (bottom) distance for each time interval.
3-6 0-3 6-9
A runner traveling at 8 m/s begins to slow down by accelerating at --1 m/s2 for 4 seconds. Without the acceleration the runner would have ran m during those 4 seconds, but the acceleration reduced the distance by m.
32 8
A disk displaces 400 radians (rads) over an 8 second interval. The rotational velocity during that 8 second time interval was rad/s.
50
A wheel displaces 10 revolutions (revs) over a 5 second interval. The rotational velocity during that 5 second time interval was rev/s.
2
A car is traveling at a velocity of 30 m/s. The car then starts to accelerate at 5 m/s2. In the 4 seconds the car is accelerating, it gained m/s.
20
There is a simple relationship between linear velocity and rotational velocity: v = rω. In order for this relationship to be valid the rotational velocity must be expressed in per unit time.
radians
Rotational momentum is conserved when the net on a system is zero.
torque
A beam is in equilibrium with two torques acting on it: one torque is 15 N⋅m and the other torque is N⋅m.
-15
A disk is initially spinning with a rotational velocity of 16 rad/s. The disk's rotational velocity is decreased to 10 rad/s over a 2 second interval. The rotational acceleration during that two second time interval was rad/s2.
-3
Let us consider a unit circle (a circle of radius 1). The circumference of that circle is 2π, which is the number of radians in a full circle. Given in degrees instead of radians, one full circle is degrees. Thus, to convert degrees to radians we multiply the number of degrees times 2π3602π360.
360
A disk is initially spinning with a rotational velocity of 6 rad/s. The disk's rotational velocity is increased to 14 rad/s over a 2 second interval. The rotational acceleration during that two second time interval was rad/s2.
4
The plot depicts the position versus time of a toy car in one dimension. During which time interval(s) is the car going backward?
4--6 seconds 0--2 seconds
Rank the instantaneous acceleration at the times below in order from the largest positive acceleration (top) to the largest negative acceleration (bottom).
6 8 2
Which of the following quantities are forces?
6--8 seconds 0--2 seconds
The adjoining graph shows the velocity vs time of a go-kart. At which time(s) is the go-kart at rest?
8 seconds 2 seconds
The velocity versus time graph is for a car traveling in one dimension. During which interval(s) is the car traveling only backward?
8--10 seconds 6--8 seconds
A child on a pivot stool holds two weights, one in each hand. Will the moment of inertia be greater when the child holds the weights close to her body or when she holds them away from her body?
Away from her body.
Rank the adjoining velocity versus time plots of four toy cars in order from most distance covered (top) to least distance covered (bottom).
BCDA
The direction of positive torque is arbitrary. For this question we will use counterclockwise as the direction in which the torque must cause the change in rotation in order for it to be positive; otherwise, the torque is negative. Which of the forces in the picture will produce a negative torque?
C D
Which quantities are important when trying to balance a scale?
The distance of the masses from the fulcrum. The weight of the masses.
Both rotational velocity and rotational acceleration are rates of change, but simply dividing the change in angle or the change in rotational velocity by the time it takes to make the change will result in rates of change. If the instantaneous rate is required then the time interval must be made very
average small
Rank the following uniform objects of all the same mass based on their moment of inertia about their center, from largest moment of inertia (top) to the smallest moment of inertia (bottom).
a ring a solid
Rank the following uniform objects of all the same mass based on their moment of inertia about their center from largest moment of inertia (top) to the smallest moment of inertia (bottom).
a spherical shell of radius a solid sphere of radius
Match the linear quantities on the left with the analogous rotational quantity on the right.
a=a v=w d=o
Both rotational velocity and rotational acceleration are rates of change, but simply dividing the change in angle or the change in rotational velocity by the time it takes to make the change will result in rates of change. If the instantaneous rate is required then the time interval must be made very .
average small
Both rotational velocity and rotational acceleration are rates of change, but simply dividing the change in angle or the change in rotational velocity by the time it takes to make the change will result in rates of change. If the instantaneous rate is required then the time interval must be made very
averager small
For the three objects in the illustration, rank the objects by the size of their linear acceleration from largest (top) to smallest (bottom) of the boxes, given that the disk is spinning with constant rotational acceleration.
box 3 box 2 box 1
When a planet is far from the sun, the planet's moment of inertia is large and its rotational velocity is small. When the planet is closer to the sun its moment of inertia decreases, which means its rotational velocity _____. This is due to the net torque from gravity being zero and thus rotational momentum being conserved.
increases
The resistance an object has to changing its rotational state is called its rotational .
inertia
A rock at rest is dropped from the rooftop of a tall building. The acceleration of the rock is around 10 m/s2 downwards. The distance fallen by the rock during a 1 second time interval is
largest during the last second of falling.
The torque on an object depends on
lever arm force
The rotational momentum, L, is
lw
Match the conservation law with its condition
rotational momentum=No net torque acting on the system. linear momentum=No net force acting on the system. No net force acting on the system. energy=No forces doing work on the system. No forces doing work on the system.
The rotational acceleration is the rate of change of the
rotational velocity
When a stationary bicycle starts to tip over
the rotational momentum of the tipping is the only rotational momentum, so the bike just falls.
A student sits with a rotating wheel on a stool with negligible friction. The student flips the wheel. The rotational momentum of the wheel now points downwards. The student starts to rotate in the opposite direction as the wheel with a rotational momentum that is the magnitude of the wheel's rotational momentum, to conserve rotational momentum.
twice
The force of gravity is attractive, which makes the lever arm distance zero. Thus, the net torque on a planet due to the sun's gravity is .
zero
Which of the following Greek letters are used to represent different aspects of rotational motion?
α ω θ
Which equation would be good to find how long an object had been rotating if you knew the rotational acceleration, the rotational displacement, and that the object had started from rest?
θ=ωit+1212αt2
Which equation would be good to find the rotational acceleration if we already knew the initial rotational velocity, the rotational displacement, and the final rotational velocity?
ω2=ωi2+2αθ
Which equation would be good to find the initial rotational velocity if you knew the rotational acceleration, the amount of time the object had been accelerating, and the final rotational velocity?
ω=ωi+αt