Centrifuge A centrifuge with a 0.40-kg ·m^2 rotational inertia has a rotational acceleration of

Name: Problem 20, Chapter 8: College Physics
Uploaded: 2020-04-15T08:03:43-08:00
Duration: 1 min 1 s
Channel: Salamat Ali
Description: Centrifuge A centrifuge with a 0.40-kg ·m^2 rotational inertia has a rotational acceleration of 100 rad / s^2 when the power is turned on. (a) Determine the minimum torque that the motor supplies. (b) What time interval is needed for the centrifuge's rotational velocity to increase from zero to 5000 rad / s ?

step 1 Part A of the given problem, we are asked to find the torque. So torque from the definition is g

Question

Centrifuge A centrifuge with a $0.40-\mathrm{kg} \cdot \mathrm{m}^{2}$ rotational inertia has a rotational acceleration of 100 $\mathrm{rad} / \mathrm{s}^{2}$ when the power is turned on. (a) Determine the minimum torque that the motor supplies. (b) What time interval is needed for the centrifuge's rotational velocity to increase from zero to 5000 $\mathrm{rad} / \mathrm{s} ?$

   Centrifuge A centrifuge with a $0.40-\mathrm{kg} \cdot \mathrm{m}^{2}$ rotational inertia has a rotational acceleration of 100 $\mathrm{rad} / \mathrm{s}^{2}$ when the
power is turned on. (a) Determine the minimum torque
that the motor supplies. (b) What time interval is needed
for the centrifuge's rotational velocity to increase from zero
to 5000 $\mathrm{rad} / \mathrm{s} ?$

College Physics

Eugenia Etkina,… 1st Edition

Chapter 8, Problem 20

Instant Answer

Solved by Expert Salamat Ali

04/15/2020

Step 1

40 \, \mathrm{kg} \cdot \mathrm{m}^{2}$ and the rotational acceleration (α) as $100 \, \mathrm{rad} / \mathrm{s}^{2}$. We can use the formula for torque (τ) which is given by the product of rotational inertia and rotational acceleration. Mathematically, it is Show more…

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Centrifuge A centrifuge with a $0.40-\mathrm{kg} \cdot \mathrm{m}^{2}$ rotational inertia has a rotational acceleration of 100 $\mathrm{rad} / \mathrm{s}^{2}$ when the power is turned on. (a) Determine the minimum torque that the motor supplies. (b) What time interval is needed for the centrifuge's rotational velocity to increase from zero to 5000 $\mathrm{rad} / \mathrm{s} ?$

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Key Concepts

Angular Kinematics

Angular kinematics deals with the motion of objects in rotation, including how angular velocity changes over time under constant angular acceleration. It involves equations analogous to those in linear kinematics, determining quantities such as the time required for an object to reach a certain angular speed from rest under constant acceleration. This concept is used to calculate the time interval needed for rotational speed changes.

Rotational Dynamics

Rotational dynamics concerns the relationship between torque, moment of inertia, and angular acceleration. A key equation in this domain is ? = I?, which states that the net torque acting on an object is equal to its moment of inertia multiplied by its angular acceleration. This concept is crucial for understanding how motors or other forces cause rotational motion in systems such as centrifuges.

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