The 75 -kg flywheel has a radius of gyration about its shaft axis of k̅=0.50 m and is subjected

Name: Problem 168, Chapter 6: Engineering Mechanics: Dynamics
Uploaded: 2021-01-29T13:11:00-08:00
Duration: 1 min 18 s
Channel: Narayan Hari
Description: The 75 -kg flywheel has a radius of gyration about its shaft axis of k̅=0.50 m and is subjected to the torque M=10(1-e^-t) N ·m, where t is in seconds. If the flywheel is at rest at time t=0 determine its angular velocity ωat t=3 s.

step 1 In this question given that, so we have given the mass value as 75 kg, k is given as 0 .5 meter

Question

The 75 -kg flywheel has a radius of gyration about its shaft axis of $\bar{k}=0.50 \mathrm{m}$ and is subjected to the torque $M=10\left(1-e^{-t}\right) \mathrm{N} \cdot \mathrm{m},$ where $t$ is in seconds. If the flywheel is at rest at time $t=0$ determine its angular velocity $\omega$ at $t=3$ s.

   The 75 -kg flywheel has a radius of gyration about its shaft axis of $\bar{k}=0.50 \mathrm{m}$ and is subjected to the torque $M=10\left(1-e^{-t}\right) \mathrm{N} \cdot \mathrm{m},$ where $t$ is in seconds. If the flywheel is at rest at time $t=0$ determine its angular velocity $\omega$ at $t=3$ s.

Engineering Mechanics: Dynamics

J. L. Meriam, L. G.… 8th Edition

Chapter 6, Problem 168

Instant Answer

Solved by Expert Narayan Hari

01/29/2021

Step 1

Step 1: The angular momentum equation can be written as: \[I\frac{d\omega}{dt} = M\] where $I$ is the moment of inertia, $\omega$ is the angular velocity, and $M$ is the torque. Show more…

Show all steps

Thanks for your feedback!

The 75 -kg flywheel has a radius of gyration about its shaft axis of $\bar{k}=0.50 \mathrm{m}$ and is subjected to the torque $M=10\left(1-e^{-t}\right) \mathrm{N} \cdot \mathrm{m},$ where $t$ is in seconds. If the flywheel is at rest at time $t=0$ determine its angular velocity $\omega$ at $t=3$ s.

Play audio

Feedback

Narayan Hari and 79 other subject Physics 101 Mechanics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Newton's Second Law for Rotation

Newton's second law for rotation relates the net torque acting on an object to its angular acceleration, expressed by the equation M = I * ?. This law provides the framework for understanding how applied torques affect the rotational speed of an object.

Time-Dependent Torque and Integration

When the applied torque changes with time, the resulting angular acceleration is also time-dependent. To determine the angular velocity at a specific time, one must integrate the angular acceleration over time, taking into account the functional form of the torque and the initial conditions.

Moment of Inertia

The moment of inertia is a measure of an object's resistance to changes in its rotational motion and depends on both its mass and how that mass is distributed relative to the axis of rotation. It can be calculated using the formula I = m * k^2, where m is the mass and k is the radius of gyration.

Please give Ace some feedback