• :00Days
  • :00Hours
  • :00Mins
  • 00Seconds
A new era for learning is coming soonSign up for free
Log In Start studying!

Select your language

Suggested languages for you:
Deutsch (DE)
Deutsch (UK)
Deutsch (US)

Americas

Europe

Answers without the blur. Sign up and see all textbooks for free! → Illustration

8-13P

Expert-verified
Physics Principles with Applications
Found in: Page 198
Physics Principles with Applications

Physics Principles with Applications

Book edition 7th
Author(s) Douglas C. Giancoli
Pages 978 pages
ISBN 978-0321625922

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later
Illustration

Short Answer

How fast (in rpm) must a centrifuge rotate if a particle 8.0 cm from the axis of rotation is to experience an acceleration of 100,000 g’s?

The number of revolutions per minute is 33422.5 rpm.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Given data

The distance from the axis of rotation is \({\rm{r}} = 8\;{\rm{cm}}\).

The acceleration is \({\rm{a}} = 100000{\rm{g}}\)

 Angular velocity and acceleration

In this problem, to calculate the revolutions per minute of a centrifuge, the relation between radial acceleration and angular velocity will be utilized.

Determine the revolutions per minute

The relation to calculate the revolutions per minute is given by:

\(\omega = \sqrt {\frac{a}{r}} \)

Here, r is the radius of the wheel and \(\omega \) is the angular speed.

On plugging the values in the above relation, you get:

\(\begin{aligned}{l}\omega &= \sqrt {\frac{{100000 \times 9.8\;{\rm{m/}}{{\rm{s}}^2}}}{{\left( {8\;{\rm{cm}} \times \frac{{1\;{\rm{m}}}}{{100\;{\rm{cm}}}}} \right)}}} \\\omega &= \left( {3500\;{\rm{rad/s}} \times \frac{{60\;{\rm{rpm}}}}{{2\pi \;{\rm{rad/s}}}}} \right)\\\omega &= 33422.5\;{\rm{rpm}}\end{aligned}\)

Thus, \(\omega = 33422.5\;{\rm{rpm}}\) is the correct answer.

Most popular questions for Physics Textbooks

A wheel of mass M has radius R. It is standing vertically on the floor, and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–60). The step has height h, where h < R. What minimum force F is needed?

If the coefficient of static friction between a car’s tires and the pavement is 0.65, calculate the minimum torque that must be applied to the 66-cm-diameter tire of a 1080-kg automobile in order to “lay rubber” (make the wheels spin, slipping as the car accelerates). Assume each wheel supports an equal share of the weight.

A bicycle odometer (which counts revolutions and is calibrated to report distance traveled) is attached near the wheel axle and is calibrated for 27-inch wheels. What happens if you use it on a bicycle with 24-inch wheels?

A small 350-gram ball on the end of a thin, light rod is rotated in a horizontal circle of a radius of 1.2 m. Calculate (a) the moment of inertia of the ball about the center of the circle and (b) the torque needed to keep the ball rotating at a constant angular velocity if the air resistance exerts a force of 0.020 N on the ball. Ignore the air resistance on the rod and its moment of inertia.

In traveling to the Moon, astronauts aboard the Apollo spacecraft put the spacecraft into a slow rotation to distribute the Sun’s energy evenly (so one side would not become too hot). At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. Think of the spacecraft as a cylinder with a diameter of 8.5 m rotating about its cylindrical axis. Determine (a) the angular acceleration, and (b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 6.0 min after it started this acceleration.
Icon

Want to see more solutions like these?

Sign up for free to discover our expert answers
Get Started - It’s free

Recommended explanations on Physics Textbooks

Work Energy and Power

Read explanation

Radiation

Read explanation

Astrophysics

Read explanation

Physics of Motion

Read explanation

Scientific Method Physics

Read explanation

Famous Physicists

Read explanation

Fluids

Read explanation

Torque and Rotational Motion

Read explanation

Nuclear Physics

Read explanation

Fields in Physics

Read explanation

Measurements

Read explanation

Space Physics

Read explanation

Electricity

Read explanation

Physical Quantities and Units

Read explanation

Medical Physics

Read explanation

Electrostatics

Read explanation

Further Mechanics and Thermal Physics

Read explanation

Mechanics and Materials

Read explanation

Engineering Physics

Read explanation

Energy Physics

Read explanation

Force

Read explanation

Particle Model of Matter

Read explanation

Waves Physics

Read explanation

Magnetism

Read explanation

Modern Physics

Read explanation

Atoms and Radioactivity

Read explanation

Dynamics

Read explanation

Electricity and Magnetism

Read explanation

Conservation of Energy and Momentum

Read explanation

Fundamentals of Physics

Read explanation

Kinematics Physics

Read explanation

Circular Motion and Gravitation

Read explanation

Linear Momentum

Read explanation

Rotational Dynamics

Read explanation

Oscillations

Read explanation

Translational Dynamics

Read explanation

Geometrical and Physical Optics

Read explanation

Thermodynamics

Read explanation

Magnetism and Electromagnetic Induction

Read explanation

Electromagnetism

Read explanation

Electric Charge Field and Potential

Read explanation

Turning Points in Physics

Read explanation

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.