Torque - PowerPoint Presentation

Slide1

Torque

A

torque

is an action that causes objects to rotate.

Torque is

not

the same thing as force.

For rotational motion, the torque

is what is most directly related to the motion, not the force.Slide2

Torque

Motion in which an entire object moves is called

translation

. Motion in which an object spins is called rotation.The point or line about which an object turns is its center of rotation.An object can rotate and translate.Slide3

Torque

Torque

is created when the

line of action of a force does not pass through the center of rotation.The line of action is an imaginary line that follows the direction of a force and passes though its point of application.Slide4

Torque

To get the maximum torque, the force should be applied in a direction that creates the greatest

lever arm.

The lever arm is the perpendicular distance between the line of action of the force and the center of rotationSlide5
Slide6

Torque

t

= r x F

Lever arm length (m)

Force (N)

Torque (N

.

m)Slide7

Calculate a torque

A force of 50 newtons is applied to a wrench that is 30 centimeters long.

Calculate the torque if the force is applied perpendicular to the wrench so the lever arm is 30 cm.Slide8

Rotational Equilibrium

When an object is in rotational equilibrium, the net torque applied to it is zero.

Rotational equilibrium is often used to determine unknown forces.

What are the forces (FA, FB) holding the bridge up at either end?Slide9

Rotational EquilibriumSlide10

Calculate using equilibrium

A boy and his cat sit on a seesaw.

The cat has a mass of 4 kg and sits 2 m from the center of rotation.

If the boy has a mass of 50 kg, where should he sit so that the see-saw will balance?Slide11

When

the force and lever arm are NOT perpendicularSlide12

Calculate

a torque

It takes 50 newtons to loosen the bolt when the force is applied perpendicular to the wrench.

How much force would it take if the force was applied at a 30-degree angle from perpendicular?

A 20-centimeter wrench is used to loosen a bolt.

The force is applied 0.20 m from the bolt.Slide13

Center

of Mass

Key Question:

How do objects balance?Slide14

Center of Mass

There are three different axes about which an object will naturally spin.

The point at which the three axes intersect is called the

center of mass.Slide15

Finding the center of mass

If an object is irregularly shaped, the center of mass can be found by spinning the object and finding the intersection of the three spin axes.

There is

not always material at an object’s center of mass.Slide16
Slide17

Finding

the center of gravity

The center of gravity of an irregularly shaped object can be found by suspending it from two or more points.For very tall objects, such as skyscrapers, the acceleration due to gravity may be slightly different at points throughout the object.Slide18

Balance and center of mass

For an object to remain upright, its center of gravity must be

above

its area of support. The area of support includes the entire region surrounded by the actual supports.An object will topple over if its center of mass is not above its area of support.Slide19
Slide20

Rotational

Inertia

Key Question:

Does mass resist rotation the way it resists acceleration?Slide21

Rotational Inertia

Inertia is the name for an object’s resistance to a change in its motion (or lack of motion).

Rotational inertia

is the term used to describe an object’s resistance to a change in its rotational motion. An object’s rotational inertia depends not only on the total mass, but also on the way mass is distributed.Slide22

Linear

and Angular Acceleration

a =

a

r

Radius of motion

(m)

Linear

acceleration

(m/sec

2

)

Angular acceleration (kg)Slide23

Rotational Inertia

To put the equation into rotational motion variables, the

force

is replaced by the torque about the center of rotation.The linear acceleration is replaced by the angular acceleration.Slide24

Rotational

Inertia

A rotating mass on a rod can be described with variables from linear or rotational motion.Slide25

Rotational

Inertia

The product of mass × radius squared (

mr2) is the rotational inertia for a point mass where r is measured from the axis of rotation.Slide26

Moment

of Inertia

The sum of mr

2 for all the particles of mass in a solid is called the moment of inertia (I). A solid object contains mass distributed at different distances from the center of rotation. Because rotational inertia depends on the square of the radius, the distribution of mass makes a big difference for solid objects.Slide27

Moment

of Inertia

The

moment of inertia

of some simple shapes rotated around axes that pass through their centers.Slide28

Rotation

and Newton's 2nd Law

If you apply a torque to a wheel, it will spin in the direction of the torque.

The greater the torque, the greater the angular acceleration.Slide29

Angular

Momentum

Investigation Key Question:

How does the first law apply to rotational motion?Slide30

Angular Momentum

Momentum resulting from an object moving in linear motion is called

linear momentum

. Momentum resulting from the rotation (or spin) of an object is called angular momentum.Slide31

Conservation

of Angular Momentum

Angular momentum is important because it obeys a conservation law, as does linear momentum.

The total angular momentum of a closed system stays the same.Slide32

Calculating

angular momentum

Angular momentum is calculated in a similar way to linear momentum, except the mass and velocity are replaced by the moment of inertia and angular velocity.

Angular

velocity

(rad/sec)

Angular

momentum

(kg m/sec

2

)

L =

I

w

Moment of inertia

(kg m

2

)Slide33

Calculating

angular momentum

The moment of inertia of an object is the average of mass times radius squared for the whole object.

Since the radius is measured from the axis of rotation, the moment of inertia depends on the axis of rotation.Slide34

You are asked for angular momentum.

You are given mass, shape, and angular velocity.

Hint: both rotate about y axis.

Use L= I

, Ihoop = mr2,

Ibar = 1/12

ml

2

Calculating angular momentum

An artist is making a moving metal sculpture. She takes two identical 1 kg metal bars and bends one into a hoop with a radius of 0.16 m. The hoop spins like a wheel. The other bar is left straight with a length of 1 meter. The straight bar spins around its center. Both have an angular velocity of 1 rad/sec. Calculate the angular momentum of each and decide which would be harder to stop.Slide35

Solve hoop:

I

hoop

= (1 kg) (0.16 m)2 = 0.026 kg m2L

hoop= (1 rad/s) (0.026 kg m2) = 0.026 kg m2/sSolve bar:

Ibar = (1/12

)(1 kg) (1 m)

2

= 0.083 kg m

2

L

bar

= (1 rad/s) (0.083 kg m

2

) = 0.083 kg m

2

/s

The bar has more than 3x the angular momentum of the hoop, so it is harder to stop.

Calculating angular momentum