What is the turntable's angular velocity, in rpm, just after this event?

Rolling Motion & Angular Momentum

4/2/2108

1

Table Challenge 5

A pencil has mass M and length L. It is standing straight up on a table on its eraser end. A slight push causes the pencil to fall over. Friction between the eraser and the table provides a pivot point.

Find an expression for the speed of the tip of the pencil as it hits the table.

2

Mass M

Length L

Pivot

Point

Rolling motion without slipping is difficult to describe with kinematics

So instead, use energy

The text describes rolling as:

Rotational kinetic energy can be added in with translations to find the total kinetic energy of an object:

Rolling Motion

3

Gotta Go Fast

4

We’ll be taking a look at the rolling motion of 4 different objects:

Solid Sphere, Hollow Sphere, Solid Cylinder, Hollow Cylinder

Using the materials provided, set up an incline plane and rank the speeds of the objects from fastest (shortest time) to slowest (longest time)

When finished, record your ranking on LC

4

An Analysis of Motion

There are several ways you can find how long it takes an object to slide down an incline without friction…

What about for rolling motion?

5

0

1

L

y = 0

From 1D Kinematics for x-axis parallel to incline:

Conserve energy 0 to 1:

Whiteboard Problem 12-14

Find an expression for the time it takes for a solid sphere to go down an incline with no rolling friction. Assume that the object is rotating about its center of mass, so that the moment of inertia can be found in a table. Your expression should look like:

Enter your number in (LC)

6

Whiteboard Problem 12-5

A marble starts from rest and rolls down the track shown around the loop-the-loop of radius R. The marble has mass m and radius r.

Find an expression for the minimum height h that the track must have for the marble to make it around the loop without falling off. (LC)

7

Angular Momentum

When an object rotates, it has rotational kinetic energy

It will also have angular momentum.

8

For a particle:

Uniform Circular Motion:

Rigid Body rotating about a fixed symmetry axis:

The vectors in the rigid body momentum just indicate direction as ccw or cw

8

Conservation of Angular Momentum

Recall that Newton’s second law could be written in terms of momentum

So then for a rotating system:

Which if there are no net torques…

9

In Summary

Kinematics:

Dynamics:

Energy:

Momentum:

10

Constant Acceleration

(particle)

(rigid body)

10

Whiteboard Problem 12-16

A 2.0kg, 20cm diameter turntable rotates at 100 rpm on frictionless bearings. Two 500g blocks fall from above, hit the turntable simultaneously at the opposite end of a diameter, and stick.

What is the turntable’s angular velocity, in rpm, after this event? (LC)

11

Applied Sciences

Architecture and Design

Biology

Business & Finance

Chemistry

Computer Science

Geography

Geology

Education

Engineering

English

Environmental science

Spanish

Government

History

Human Resource Management

Information Systems

Law

Literature

Mathematics

Nursing

Physics

Political Science

Psychology

Reading

Science

Social Science

Home

Blog

Archive

Contact

google+twitterfacebook

Copyright © 2019 HomeworkMarket.com