rotational n.2 torque · department of physics and applied physics phys.1410 lecture 20 a.danylov...

DepartmentofPhysicsandAppliedPhysicsPHYS.1410Lecture20A.Danylov

Lecture 20

Chapter 12

Rotational N.2nd LawTorque

Physics I

Newton 2nd Law again!?That’s it. He crossed the line!

Course website:https://sites.uml.edu/andriy-danylov/teaching/physics-i/


Today we are going to discuss:

Chapter 12:

Torque: Section 12.5 Gravitational Torque: Section 12.5 Rotational Newton’s 2nd Law: Section 12.6

IN THIS CHAPTER, you will continue discussing rotational dynamics


Rotational Dynamics

What causes rotation?


Why? What causes rotation?

There are three parameters (lever arm, force, and Arm positioning (angle)) seem to

be very helpful in rotating doors.

When we apply the force, the door turns on its hinges (a turning effect is produced).

In the 1st case, we are able to open the door with ease.

In the 2nd case, we have to apply much more force to cause the same turning effect.

Let’s construct a new quantity out of them

Torque is a turning force (the rotational equivalent of force).

It should depend on force, lever arm, angle:

(definition)

rF sin

F

Axis of rotation

Sign of a torque convention:A positive torque tries to rotate an object in a CCW directionA negative torque tries to rotate an object in a CW direction

r

r

F

With the vector product notation we can rewrite torque as


There are two ways of looking at Torque:

)sin( FrLet’s arrange it like this:

Perpendicular component of force acting at a distance r from the axis

1 )( Fr

rF sinF

F

r

F

r

r F(rsin )

sinrLine of force (action)

Or Let’s arrange it like this:

Force times arm lever extending from the axis to the line of force and perpendicular to the

line of force

2 )( rF


TorqueExampleA 2.0-m-long uniform beam (m=5 kg) shown in the figure lies on the frictionless table. Four forces shown in the figure are applied to the beam which can rotate about the axis going through its left end. The second force, F2, is applied perpendicularly at the point of the CM. Calculate the net torque about the axis shown in the figure.

You are using a wrench to loosen

a rusty nut. Which arrangement

will be the most effective in

loosening the nut?

A

C D

B

Because the forces are all the same, the only difference is the lever arm. The arrangement with the largest lever arm (case #2) will provide the largest torque.

E) all are equally effective

Follow-up: What is the difference between arrangement A and D?

ConcepTest Loosening Nuts

r

Line of force (action)

)( rF F(rsin )


TorqueExampleThe body shown in the figure is pivoted at O. Three forces act on it in the direction shown in the figure: FA=10 N at point A, 8.0 m from O; FB=10 N at point B, 4.0 m from O and FC=19 N at point C, 3.0 m from O. Calculate the net torque about point O.

Skip it


Torque due to Gravity

gMW CMR

The proofCM

We often encounter systems in which there is a torque exerted by gravity.

(Read only if you want)

The torque due to gravity is found by treating the object as if all its mass is concentrated at the center of mass.

An object will balance on a pivot only If the CM is directly above the pivot point. If the pivot point is not under the CM, the grav. torquewill cause the object to rotate

Example

MgSinRCMgrav


Torque causes angular acceleration:

Force causes linear acceleration: (Translational N.2nd law)

Newton’s 2nd law of rotation

I

I is the Moment of Inertia(rotational equivalent of mass)

amF

Angular accelerationTorque

(rotational equivalent of force)

(Rotational N.2nd law)


Falling rodExampleWhat is the angular acceleration of the rod, if it is released from rest,

at the moment it is released? What is the linear acceleration of the tip?

End of the class

ConcepTest Closing a DoorA

B

C

D

E

The diagram shows the top view of a door, hinge to the left and door-knob to the right. The same force F is applied differently to the door. In which case is the torque provided by the applied force about the rotation axis greatest?

The torque is =Fd sin , and so the force that is at 90° to the lever arm is the one that will have the largest torque. (Clearly, to close the door, you want to push perpendicularly!!) So A or B? B has larger lever arm

A B C

D

E


Thank you

rotational n.2 torque · department of physics and applied physics phys.1410 lecture 20 a.danylov...

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