A 10.0- kg cylinder rolls without slipping on a rough surface.At an instant when its center of gravity has a speed of 10.0 m/s,determine (a) the translational kinetic energy of its center ofgravity, (b) the rotational kinetic energy about its center ofgravity, and (c) its total kinetic energy.

Question
Asked Dec 19, 2019
1 views

A 10.0- kg cylinder rolls without slipping on a rough surface.
At an instant when its center of gravity has a speed of 10.0 m/s,
determine (a) the translational kinetic energy of its center of
gravity, (b) the rotational kinetic energy about its center of
gravity, and (c) its total kinetic energy.

check_circle

Expert Answer

Step 1

(a) 

help_outline

Image Transcriptionclose

Given info: The mass of the cylinder is 10.0 kg and the speed of center of gravity of the cylinder is 10.0 m/s. Explanation: The formula for the translational kinetic energy is, KE: = mv? m is mass of the cylinder. Vz is translational speed of the cylinder. Substitute 10.0 kg for m and 10.0 m/s for vų to find KEț. KE, = }(10.0 kg) (10.0 m/s)² = 500 J Thus, the translational kinetic energy of the center of gravity of the cylinder is 500 J.

fullscreen
Step 2

(b)

...
help_outline

Image Transcriptionclose

Explanation: The angular speed of the cylinder is related to its translational speed as w = vt/r and the moment of inertia of the cylinder is I = mr2 /2. By using these relations, the rotational kinetic energy (KE, = Iw? /2) of the cylinder is calculated. The formula for the translational kinetic energy is, KE, = mv? m is mass of the cylinder. Vt is translational speed of the cylinder. Substitute 10.0 kg for m and 10.0 m/s for v; to find KE,. KE, = (10.0 kg) (10.0 m/s)² = 250 J %3D Thus, the rotational kinetic energy of the center of gravity of the cylinder is 250 J.

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Science

Physics

Related Physics Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: A voltmeter connected across the terminals of a tungsten -filament light bulb measures 115 V when an...

A: Part A:

question_answer

Q: In the Bohr model of the hydrogen atom, an electron in thelowest energy state moves at a speed equal...

A: Click to see the answer

question_answer

Q: As a 75.0 - kg man steps onto a bathroom scale, the springinside the scale compresses by 0.650 mm. E...

A: (a) Spring constant is,

question_answer

Q: Apollo 14 astronaut Alan Shepard famously took two golfshots on the Moon where it’s been estimated t...

A: Given:Mass of the projectile ball, m = 0.045 kgRange = 4 km = 4000 mAngle of projection = 45 degrees...

question_answer

Q: We have seen that an electric field must exist inside a conductorthat carries a current. How is that...

A: in this case, the potential difference between the end of the wire causes the electrons to flow and ...

question_answer

Q: An approximate model fora ceiling fan consists of acylindrical disk with fourthin rods extending fro...

A: Given data:Mass of the disc, m = 2.50 kgRadius of the disc, r = 0.200 mMass of each rod, M = 0.850 k...

question_answer

Q: A object of mass 3.00 kg is subject to a force Fx that varies with position as in the figure below. ...

A: Given,

question_answer

Q: Does the string that supports a pendulum bob do work on the bob as it swings to and fro? Does the fo...

A: The string applies a force of tension on the bob, which is perpendicular to the bob. When the bob mo...

question_answer

Q: A model airplane with mass 0.750 kg is tethered by a wire sothat it flies in a circle 30.0 m in radi...

A: Click to see the answer