Chapter 8: Rotational Motion (from Lecture Slide) Flashcards
When an object turns about an internal axis, it is undergoing
Circular motion or rotation
Circular motion is characterized by two kinds of speeds
1) Tangential (linear) speed
2) Rotational (angular) speed
Rotational speed is
The number of rotations or revolutions per unit of time
All parts of a rigid turntable turn about the axis of rotation in
The same amount of time
All points have the same
Angular/rotational speed
Tangential speed
The linear speed of something moving along a circular path
At different radii, the tangential speeds
Can be vary
Rotational inertia
The property of an object to resist changes in its rotational state of motion
An object rotating about an axis tends to remain rotating about
The same axis at the same rotational speed unless interfered with by some external influence
Bodies that are rotating tend to remain what?
Rotating
Non-rotating bodies tends to remain what?
Non-rotating
Like linear rotation, rotational inertia depends on
Mass: Distribution of the mass about the axis of rotation
The greater the distance between an object’s mass concentration and the axis
The greater the rotational inertia
The greater the rotational inertia of an object
The greater the difficulty in changing its rotational state
Much of the mass of the pole is far from
The axis of rotation (its midpoint)
- Depends upon the axis around which it rotates
a. Easier: to rotate around an axis passing through it (mass is evenly distributed around axis)
- Depends upon the axis around which it rotates
b. Harder: to rotate it around vertical axis passing through center (half of its mass is distributed on both sides of the axis)
- Depends upon the axis around which it rotates
c. Hardest: to rotate it around vertical axis passing through the end (all mass is on one side of the axis)
Torque is
The rotational counterpart of force
Force tends to
Change the motion of things
Torque depends upon three factors:
1) Magnitude of the force
2) The direction in which the force acts
3) The point at which the force is applied on the object
Torque (like rotational inertia) involves distance from the rotational axis. This distance is called the
Lever arm
The tendency of a force to cause rotation is called
Torque
Lever arm is less than
Length of handle because of direction of force
Lever arm is equal to
Length of handle
Lever arm is longer than
Length of handle
If the force is applied in the same direction as the perpendicular distance or at the axis of rotation, which force produces no torque?
It does not rotating anything
If the seesaw doesn’t rotate, does that mean that there’s no torque?
Like Newton 1st law, you can still have force but have zero net force
Similarly, you can still have torques, produces but having what?
Zero net torque
Center of mass
The average position of all the mass that makes up the object
Symmetric object, the mass is located at
The geometric center
Asymmetric (irregular) object depends on
The position, bat, were thicker end
Center of gravity
The average position of weight distribution and located at the same point as the CM
Two types of motion
1) Straight line motion along its CM
2) Rotation about its CM
Locating the center of gravity
1) Is at geometric midpoint
2) Balancing objects provides a way to find CG
3) All points produce a resultant weight vector at the CG
4) Supporting the midpoint supports the entire stick
Stability
The location of the center of gravity is important for stability
If we draw a line straight down from the center of gravity and it falls
Inside the base of support of the object, it is in stable equilibrium and it will balance.
If it falls outside the base, it is
Unstable
Both L-shaped objects have the same weight. Are they in equilibrium?
A torque exists in both and their line of gravity falls outside the base of support, so they tend to rotate, both are unstable and both fall over
Centripetal force
Any force directed toward a fixed center
Centripetal means
Center-seeking or toward the center
Centripetal force depends upon
1) Mass of object
2) Tangential speed of the object
3) Radius of the circle
Centripetal force deals with any force that is
Directed towards the center
If the motion is circular and at constant speed, this force is
At right angle, to the path of the moving object
Greater speed and greater mass require
Greater centripetal force
Traveling in a circular path with a smaller radius of curvature requires
A greater centripetal force
When a car rounds a curve, the centripetal force prevents it from
Skidding off the road (friction force)
If the road is wet, or if the car is going too fast, the centripetal force is
Insufficient to prevent skidding off the road
Only two forces act on the bob
1) mg, the force due to gravity
2) T, tension in the string
Net force in the vertical direction of the centripetal force is
Zero
Vertical direction must be
Equal and opposite to mg
Horizontal force is the net force on the bob that contributes to the
Centripetal force
Although centripetal force is center directed, an occupant inside a rotating system seems to
Experience an outward force
This apparent outward force on a rotating or revolving body is called
Centrifugal force
Centrifugal means
Center-fleeing or away from the center
It is misconception that a centrifugal force pulls
Outward on an object
If the string break, the object doesn’t move
Radially outward
If the string break, It continues along its tangent straight-line path, because what?
No force acts on it (Newton’s First Law of Inertia)
Centrifugal force sometimes called what?
1) Fictitious force
2) Apparent force
3) Inertial force
Centrifugal force is not a real force like gravity, but
In a rotating frame, the centrifugal force feels like a real force
Centrifugal force with free fall
They don’t feel gravity anymore but they feel simulated gravity.
Simulated gravity: Stationary frame (outside)
1) Action-reaction pair between floor and person
2) If the system is defined on, the reaction froce of the floor contributes to the centripetal force
Simulated force: Rotating frame (inside)
1) No action-reaction pair exist
2) Centrifugal force acts at the center of gravity of it
3) Nothing that pulls back on it
Linear momentum
Motion along a straight line path, and called: “Inertia of motion”
Angular momentum
The “inertia of motion” of rotating objects
Angular momentum (point-like masses)
Object that is small compared with the radial distance to its axis of rotation
Rotational version of Newton’s first law: An object or system of objects will:
Maintain its angular momentum unless acted upon by an external net torque
An external net torque is required to
Change the angular momentum of an object
Our solar system has angular momentum that includes the Sun:
The spinning and orbiting planets and other smaller bodies
The angular momentum of the solar system is
Conserved unless an external torque outside the solar system changes it
In the absence of net external torques, angular momentum is
Conserved
In the absence of net external forces, linear momentum is
Conserved
If no external net torque acts on a rotating system,
The angular momentum of that system remains constant
When the man pulls the weights inward, his rotational speed
Increases
Suppose by pulling the weight inwards, the rotational inertia of the man reduces to
Half its value and the factor that would angular velocity change is double!
