7.5 Rotational Kinetic Energy

Guiding Questions:

How is total energy of a rotating object calculated?
How does torque do work to change the energy of a rotating system?

Expected Outcomes

Explain how external forces exerted on a system can exert torques to change the state of rotation of the system
Design an experiment to explore the effect of external torques on rotational kinetic energy
Calculate changes in energy of a system (rotational kinetic energy, translational kinetic energy, potential energy) when provided with angular or linear velocity and a formula to calculate rotational inertia of the system

Where does the velocity go?

Ball rolling down ramp into projectile motion, compare predicted velocity (mgh = 0.5 mv^2) to experimental velocity (range of marble and time) Where did the velocity go?

What measurements would you need to predict the location of the ball landing on the floor?

What core physics principles are necessary to answer the question?

Sketch the set-up and label the various locations of measurements and calculations necessary.

Violation of the Law of Conservation of Energy?

Where does the speed go?

Which gets to the bottom first?

Is energy conserved?

The rotational inertia of an object depends on its geometry. Typically, this is described as a fraction, some common shapes are show to the right. The derivation of the values is beyond the courses.

Translational Kinetic Energy

Rotational Kinetic Energy

where m is mass and v is velocity

where I is the moment of inertia and ω is the angular velocity

Translational Kinetic Energy v. Rotational Kinetic Energy of a Falling Disk on a String (YO-YO)

Note 23 Apr 2024.pdf

Problem Solving Guidance

Single Body about an axis

Table of Rotational Inertia Values

Single body rolling down and incline

Single body rotating about a non-center point.

Sample Problem Solving

(a) The Sun rotates on its axis once in about 27 days. Calculate the rotational kinetic energy of Sun on its axis. (M⨀ = 1.99 x 1030 kg R⨀ = 6.957 x108 m) ANS: 1.4x1036 J

(b) Calculate the rotational kinetic energy of Earth on its axis. (M🜨= 5.97×1024 kg R🜨 =6.3781×106 m) ANS: 2.57x1027 J

(c) What is the rotational kinetic energy of Earth in its orbit around the Sun? (Rorbit = 149.60 million km) ANS: 2.65x1033 J

2. Calculate the rotational kinetic energy of a 12-kg motorcycle wheel if its angular velocity is 120 rad/s and its inner radius is 0.280 m and outer radius 0.330 m. ANS: 67.42 J

3. Six small washers are spaced 10 cm apart on a rod of negligible mass and 0.5 m in length. The mass of each washer is 20 g. The rod rotates about an axis located at 25 cm, as shown.

(a) What is the moment of inertia of the system? ANS: I = 0.0035 kg ●m2

(b) If the two washers closest to the axis are removed, what is the moment of inertia of the remaining four washers? ANS: I = 0.0034 kg ●m2

4. A person rolls a bowling ball of mass 7 kg and radius 10.9 cm down a lane with a velocity of 6 m/s.

Find the rotational kinetic energy of the bowling ball, assuming it does not slip. Rot KE = 50.4 J

Find the total kinetic energy. Total KE = 176 J

5. Find the speed of a disc of radius 0.5 meters and mass 2-kg at the base of the incline. The disc starts at rest and rolls down the incline with a height of 5 meters without slipping. The incline makes a 20° angle with the horizontal surface.

6. An ice skater spins with a specific angular velocity. She brings her arms and legs closer to her body, reducing her rotational inertia to half its original value. What happens to her angular velocity? What happens to her rotational kinetic energy?

AP Classroom MCQ's

Assigned in AP Classroom.

AP Student Edition Passages

7H - Rotation KE.pdf

7G - Rotation v Translation.pdf

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