Title: Rotational Kinematics and Energy
1Rotational Kinematics and Energy
2- Angular Position, Velocity, and Acceleration
- Rotational Kinematics
- Connections Between Linear and Rotational
Quantities - Rolling Motion
- Rotational Kinetic Energy and the Moment of
Inertia - Conservation of Energy
3Angular Position, Velocity, and Acceleration
4Angular Position, Velocity, and Acceleration
Degrees and revolutions
5Angular Position, Velocity, and Acceleration
Arc length s, measured in radians
6Angular Position, Velocity, and Acceleration
7Angular Position, Velocity, and Acceleration
8Angular Position, Velocity, and Acceleration
9Angular Position, Velocity, and Acceleration
10Rotational Kinematics
If the angular acceleration is constant
11Rotational Kinematics
Analogies between linear and rotational
kinematics
12Connections Between Linear and Rotational
Quantities
13Connections Between Linear and Rotational
Quantities
14Connections Between Linear and Rotational
Quantities
15Connections Between Linear and Rotational
Quantities
This merry-go-round has both tangential and
centripetal acceleration.
16Rolling Motion
If a round object rolls without slipping, there
is a fixed relationship between the translational
and rotational speeds
17 Rolling Motion
We may also consider rolling motion to be a
combination of pure rotational and pure
translational motion
18Rotational Kinetic Energy and the Moment of
Inertia
For this mass,
19Rotational Kinetic Energy and the Moment of
Inertia
We can also write the kinetic energy as
Where I, the moment of inertia, is given by
20Rotational Kinetic Energy and the Moment of
Inertia
Moments of inertia of various regular objects can
be calculated
21Conservation of Energy
The total kinetic energy of a rolling object is
the sum of its linear and rotational kinetic
energies
The second equation makes it clear that the
kinetic energy of a rolling object is a multiple
of the kinetic energy of translation.
22Conservation of Energy
If these two objects, of the same mass and
radius, are released simultaneously, the disk
will reach the bottom first more of its
gravitational potential energy becomes
translational kinetic energy, and less rotational.
23Summary
- Describing rotational motion requires analogs to
position, velocity, and acceleration
- Average and instantaneous angular velocity
- Average and instantaneous angular acceleration
24Summary
- Period
- Counterclockwise rotations are positive,
clockwise negative - Linear and angular quantities
25Summary
- Linear and angular equations of motion
Tangential speed Centripetal acceleration Tangen
tial acceleration
26Summary
- Rolling motion
- Kinetic energy of rotation
- Moment of inertia
- Kinetic energy of an object rolling without
slipping - When solving problems involving conservation of
energy, both the rotational and linear kinetic
energy must be taken into account.