Chapter 7 physics

There must be equal amounts of mass on both sides of the center of mass (or center of
gravity) of a system.


When a rigid object rotates about a fixed axis, what is true about all the points in the object?

they all have the same angular speed, they all have the same angular acceleation

Two children, Ahmed and Jacques, ride on a merry-go-round. Ahmed is at a greater distance
from the axis of rotation than Jacques. Which of the following are true statements?
A) Jacques has a greater angular speed than Ahmed.
B) Jacques and Ahmed have the

Jacques and Ahmed have the same angular speed.
Ahmed has a greater tangential speed than Jacques.

Two forces produce equal torques on a door about the door hinge. The first force is applied at
the midpoint of the door; the second force is applied at the doorknob. Both forces are applied
perpendicular to the door. Which force has a greater magnitude?

the first force at the midpoint

Two equal-magnitude forces are applied to a door at the doorknob. The first force is applied
perpendicular to the door, and the second force is applied at 30� to the plane of the door. Which
force exerts the greater torque about the door hinge?

the first force (applied perpendicular to the door)

The moment of inertia of a uniform rod about an axis through its
center is ML2/12. The moment of inertia about an axis at one end is
ML2/3. Explain why the moment of inertia is larger about the end
than about the center.

most of the mass is distributed away from the axis of rotation

If the sum of both the external torques and the external forces on an object is zero, then the
object must be at rest.


Viewed from a point above the north pole, is the angular velocity positive or negative of earth's rotation?


For an object to be in equilibrium under the action of its own weight, the center of mass of the object must lie

directly above the base of the object

what does having the com being above the base do?

ensure that the torque due to the weight of the object will be zero about an axis passing through the point in the base

If an object is rotating clockwise, this corresponds to a _____ angular velocity.


The angular displacement of a rotating object is measured in _____.


Which factor does the torque on an object NOT depend on?
- the angle at which the force is applied
- the object's angular velocity
- the magnitude of the applied force

the object's angular velocity

moment of inertia is

the rotational equivalent of mass.

� Rotational motion

the motion of objects that spin about an axis

how do we describe rotational motion

o motion in a circle of radius r to describe its motion mathematically it is convenient to use the angle ? from the positive x-axis to describe the particle's location


� called angular position of the particle

when is theta positive in rotational motion

when measured counterclockwise from the positive x axis

when is theta negative

when measured clockwise from the positive x axis

theta is measured in angular unit


arc length is aka


arc length definition

� distance that the particle has traveled along its circular path

� The farther the particle has travled around the circle (greater the s),

the larger the angle theta in radians

when a particle travels all the way around the circle

it completes one revolution


� the arc length it travels, which is the circle's circumference 2

revolutions to degrees to radians

� 1 rev = 360 degrees = 2*pi rad

radians to degrees

� 1 rad = 1 rad
(360 degrees/2
2*pi rad) = 57.3 degrees

in linear motion a particle with a larger velocity undergoes

a greater dispalcement

o for uniform circular motion, a particle with a larger angular velocity will undergo

a greater angular displacement

angular velocity

� angular displacement through which the particle moves each second

angular velocity is constant for

a particle moving with uniform circular motion

angular speed

� absolute value of the angular velocity in circular motion

rigid body

� an extended object whose size and shape do not change as it moves
� is a good approximation for many systems

3 basic types of motion of rigid body

1) translational
2) rotational
3) combinatin

translational motion

� object as a whole moves along a trajectory but does not rotate

rotational motion

� object rotates about a fixed point. Every point on the object moves in a circle

combination motion

� an object rotates as it moves along a trajectory

every point on a rotating body has the same

angular velocity

o two points on the object at different distances from the axis of rotation will

have different speeds

o To impress his friends while riding on a carnival Ferris wheel, Paul gets out of his chair and climbs along the spoke of the wheel toward its center while the wheel continues in uniform motion. While climbing toward the center, Paul's linear speed

decreases while his angular speed remains unchanged

o Rasheed and Sofia are riding a merry-go-round that is spinning steadily. Sofia is twice as far from the axis as is Rasheed. Sofia's speed is ______ that of Rasheed.


extended object

� a system of particles for which the size and shape do make a difference and cannor be ignored

why does every point on a rotating rigid body have the same angular velocity

� all points move with the same angular velocity, but 2 points of an object have different speeds if they are at different distances from the axis of rotation

changing angular velocity is

nonuniform circular motion

angular accerlation is the _ for every point on a rotating rigid body


signs of angular accelration

o When speeding up, a and crazy w have the same sign for magnitude
o When slowing down, a and crazy w have the opposite sign of magnitude

you can have centripetal acceleration even if

angular accelation is 0

a is positive when rigid body is

� Rotating counterclockwise and speeding up
� Rotating clockwise and slowing down

a is negative when rigid body is

� Rotating counter clockwise and slowing down
� Rotating clockwise and speeding up

angular acceleration definition

o indicates how rapidly the angular velocity is changing

centripetal acceleration definition

o vector quantity that points toward the center of a particle's circular path

tangential acceleration

� Component of acceleration directed tangentially to circle
� Measures the rate at which the particle's speed around the circle changes

� because the magnitude of the velocity is increasing, the second component of the accerlation is directed tangentially

to the circle,in the same direction as the velocity


o Measure of how much force acting on an object causes that object to rotate
o Measures the effectivesness of a force at causing an object to rotate about a pivot

torque is the rotational equivalent of


what does torque depend on

� Magnitude of force
� Direction in which it acts
� The point at which it is applied on the object (distance from axis of rotation)

what is a lever arm (or moment arm)

the shortest distance between applied force and axis of rotation

o The ability of a force to cause rotation depends on the

magnitude f of the force

how to calculate torque

- use � Component of ?F that is perpendicular to the radial line causes a torque
- use � Force F with moment arm r

radial line in torque

� Starting lien at pivot and extends through the point where force is applied

f perpendicualr in torque

� tends to cause rotation of the wrench
� is the compoenent of the force that determines the torque

f parallel in torque

� points either directly toward or away from the pivot
� has no effect on the wrenche's rrotation
� contributes nothing to the torque

maximum psotiive torque for a force

� Is perpendicular to radial line

pushing straight toward the pivot exerts

zero torque

o Positive torque tries to rotate object

counterclockwise about pivot

o Pulling straight out from the pivot

exerts zero torque

o Negative torque tries to rotate the object

clockwise about the point

o Maximum negative torque for a force

is perpendicutlar to the radial line

line of action in torque

� the line that is in the direction of the force and passes through the point at which the force acts

each particle in an object expereinces

a torque due to the force of gravity

o The gravitational torque can be calculated by assuming that

the net force of gravity (object's weight) acts as a single point

single point =

center of gravity

o An object that is free to rotate about a pivot will come to rest with

the center of gravity below the pivot point

o Center of gravity tends to lie _ to the heavier objects or particles that make up the objects


� torque due to gravity when the pivot is AT the center of gravity is


_ is the force responsible for chinging the direction of the particle's velocity


o newton's 2nd law for rotational motion

� by factoring out crazy a of the sum, we're making explicit use of the fact that every particle in a rotating ridgid body has the same angular accerlation, crazy a

what is the cause of linear accelration

net force

what is the cause of angular accerlation

net torque

moment of inertia

o Rotational equivalent of mass

o It's more difficult to spin the merry go round when people sit far from the center because

it has a higher inertia than when people sit close to the center

� an object's moment of inertia depends on

the object's mass and how the mass is distrubted around the rotatin axis

rolling motion

� combination motion where an object rotates about an axis that is moving along a stright line trajectory

rolling constraint

� basic link between translation and rotation for objects that roll without slipping

o the speed of a point at the top of a wheel is

twice the speed of it's center

o the point on the bottom of a rolling object is

instantaneously at rest