Rotational Kinetic Energy (College Board AP® Physics 1: Algebra-Based)
Study Guide
Written by: Katie M
Reviewed by: Caroline Carroll
Rotational kinetic energy equation
Rotational kinetic energy is the energy associated with rotational motion
It is given by the equation:
Where:
= rotational kinetic energy, in
= rotational inertia, in
= angular velocity, in
Rotational kinetic energy, like other forms of energy, is a scalar quantity
Comparing translational and rotational energy
Rotational kinetic energy is not a new type of energy, it is a type of kinetic energy, analogous to translational kinetic energy
On a rotating body, the distribution of mass is described by its rotational inertia
The rotational inertia of an object about a fixed axis is given by:
Where:
= mass of the object, in
= distance to the axis of rotation, in
At different points on a rotating body, the translational (linear) velocity varies, but the angular velocity is the same at all points
For a single point rotating about a fixed axis, the angular speed is given by:
Where:
= linear velocity, in
Substituting these into the equation for rotational kinetic energy:
This shows that the rotational kinetic energy of an object is equivalent to its translational kinetic energy
Total kinetic energy of rigid systems
Rigid circular objects, such as wheels, move with both translational and rotational motion
For example, the wheels of a car or a bicycle rotate causing it to move forward
Newton's laws for rotational motion remain valid as long as:
the axis of rotation passes through the object's center of mass
the direction of rotation does not change
The total kinetic energy of a rigid system is a combination of:
the rotational kinetic energy due to its rotation about its center of mass
the translational kinetic energy due to the linear motion of its center of mass
This can be written as:
A rigid system can have rotational kinetic energy even if its center of mass is at rest
This is because individual points within the system can have linear speed and, therefore, kinetic energy
As a result, the whole system rotates about the stationary center of mass
Examples of this include:
flywheels
turntables
merry-go-rounds
Worked Example
A flywheel of mass and radius rotates at a constant angular velocity about an axis through its center. The rotational kinetic energy of the flywheel is .
The rotational inertia of the flywheel is .
A second flywheel of mass and radius is placed on top of the first flywheel. The new angular velocity of the combined flywheels is .
What is the new rotational kinetic energy of the combined flywheels?
A
B
C
D
The correct answer is A
Answer:
Step 1: Determine the rotational kinetic energy of the first flywheel
Step 2: Determine the total rotational inertia of the combined flywheels
Step 3: Determine the rotational kinetic energy of the combined flywheels
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