Unit 4 Flashcards
centrifugal force
- The apparent outward force on a rotating or revolving body.
- It is an effect of rotation.
- Is fictitious because it is not part of an interaction, and therefore not a true force.
- Is due to the tendency of a moving body to move in a straight-line path.
What moves faster on a disk?
Inside and outside have the same rpm, but the outside part moves faster than the inside.
Can the terms linear speed and rotational speed be used interchangeably?
No. [see sec 10.2]
A satellite is…
constantly changing direction as it travels around the Earth, and so it is constantly accelerating. B/c it is accelerating, it is experiencing a net force, gravity.
axis
straight line around which rotation takes place
Two types of circular motion
Rotation and revolution
Rotation
motion about an axis located within the body of the object
internal axis
an axis located within the body of the object
Revolution
the motion about an axis located outside the body of an object
Linear speed
distance traveled per unit of time
Tangential speed
The speed of an object moving in a circular path. Called this because the direction of motion is always tangent to the circle.
Rotational speed.
aka angular speed. Number of rotations per minute (rpm).
A point farther away from the center travels…
…a longer path in the same time, and therefore, has a greater tangential speed.
tangential speed proportion
tangential speed ~ radial distance * rotational speed or v ~ r*w
What does tangential speed depends on?
Rotational speed and the distance from the axis of rotation
Why does a moving freight train stay on the tracks?
Because their rims are slightly tapered.
An object moving in a circle still undergoes…
…an acceleration, even at a constant speed, because its direction is changing, which is due to net force.
Centripetal acceleration
What any object moving in a circle undergoes an acceleration that is directed to the center of the circle.
Centripetal
means “toward the center.”
What would happen if a centripetal force ceased to act on an object moving in a curved path?
the object would move in a straight line.
the centripetal force that holds a car in a curved path while rounding a corner comes from.
comes from the friction between the tires and the road.
When you are riding in a car and it goes around a sharp left-hand corner, why are you pressed against the door of the car?
There is no centripetal force acting to hold you in place.
What causes the centrifugal-force effect?
Inertia
In a rotating reference frame, what forces act on objects in the rotating system?
Both centripetal and centrifugal forces
Center of mass and center of gravity are…
…closely related, and for many objects, are essentially the same thing
Center of gravity
- The point at the center of an object’s weight distribution, where the force of gravity can be considered to act.
- The lower your center of gravity, the more stable you are.
An object in equilibrium has…
…no net torque acting on it.
When would the center of gravity and the center of mass be in different locations in an object?
Possibly in a very large object when the gravity varies from one part of the object to the other.
An object remains in rotational equilibrium if its center of mass is…
…above the area of support
Torque
The rotational analog of force; the product of force and the lever arm (measured in newton-meters). Tends to produce rotational acceleration.
Mechanical equilibrium rotational
sigma(torques) = 0
What does torque produce?
Rotation
Lever arm
The perpendicular distance between an axis and the line of action of a force that tends to produce rotation about that axis.
When balanced torques act on an object…
…there is no change in rotation
Center of mass
The point at the center of an object’s mass distribution, where all the mass can be considered to be concentrated
Where is center of mass located in an object?
At the point located at the object’s average position of mass.
How to apply spin to an object
A force must be applied to the edge of the object. Produces torque -> adds rotation to projectile.
Center of gravity of people
Is not located in a fixed place, but depends on body orientation.
Change in location of CG upon toppling
The center of gravity of that object is raised, lowered, or unchanged.
Unstable equilibrium
The state of an object balanced so that any small displacement or rotation lowers its center of gravity.
Stable equilibrium
The state of an object balanced so that any small displacement or rotation raises its center of gravity.
Neutral equilibrium
The state of an object balanced so that any small movement neither raises nor lowers its center of gravity.
When will an object spin/rotate?
When a force applied to an object does not pass through the object’s center of mass.
What happens when the CG of an object is raised?
the gravitational potential energy increases
Describe the conditions that are necessary so that an object will remain upright.
As long as the center of gravity of the object is above the area of support, the object will remain upright.
Explain the difference between stable, unstable, and neutral equilibrium.
In unstable equilibrium, the CG is lowered with displacement. In stable equilibrium the CG rises with displacement. In neutral equilibrium the CG neither rises nor falls with displacement.
torque equation
torque = force * lever arm
OR torque = force * distance
“objects in motion tend to stay in motion” must hold true for objects…
moving in circular paths as well.
What does inertia of a rotating object depend on?
both mass and distance
Major axes for human body
longitudinal, transverse, medial
Angular inertia
resistance to change in motion due to mass at a radial distance
Angular momentum equation
angular momentum = rotational inertia * rotational velocity
a = I*w
OR
angular momentum = mvr (mv = magnitude of linear momentum, r = radial distance)
Angular momentum
Product of rotational inertia and rotational velocity. For rotating objects. Conserved when no net torque acts on object
Rotational inertia
- aka moment of inertia.
- The resistance of an object to changes in its rotational motion.
- Is determined by the distribution of the mass of the object and the location of the axis of rotation or revolution.
The greater an object’s rotational inertia the more difficult it…
…is to change the rotational speed of an object.
Rotational inertia equation
I = mr^2 where I = rotational inertia, mass m is concentrated at the same distance r from a rotational axis
Longitudinal axis
Head-to-toe axis
Transverse axis
Rotate about it when perform somersault or flip
Media axis
Front-to-back axis
Objects of the same shape but different sizes accelerate…
equally when rolled down an incline. a = F/m
Linear momentum
Product of mass and velocity of an object. aka momentum.
Rotational velocity
Rotational speed together with a direction for the axis of rotation or revolution. Is a vector quantity with the same direction as angular momentum.
Newton’s first law of inertia for rotating systems
An object or system of objects will maintain its angular momentum (continue rotating about axis) unless acted upon by an unbalanced external torque.
Law of conservation of angular momentum
An object or system of objects will maintain a constant angular momentum unless acted upon by an unbalanced net torque.
What can simulate gravity?
In a rotating frame of reference, there seems to be an outwardly directed centrifugal force, which can simulate gravity.
What is inertia a measure of?
Laziness
What direction, when a person is in a large rotating space, is the “up” direction that a person senses is toward
the center of rotation
Equation for rotational inertia, I, of a solid sphere spinning about its axis of rotation?
l = (2/5)m*r^2
Does a hoop or a solid disk of the same diameter have a greater acceleration for down an incline?
The solid disk because it has less rotational inertia per mass.
Explain how angular momentum makes a moving bicycle easier to balance than a bicycle at rest.
The bicycle wheels at rest have no angular momentum, and the bicycle will fall over easily. When the bicycle is moving, the wheels have angular momentum, and a greater torque is required to change the direction of the angular momentum.
Centripetal Force
-Center-directed force that causes an object to move in a curved (sometimes circular) path.
-Not basic forces of nature.
-Equation: (mass*tangential speed^2)/(radius of curvature
or
F(c) = (mv^2)/r
