Rotational

MotionBELTRAN, Dave Tristan A.ELUMBA, Cherry Mae C.ESPANTO, Sharmaine P.JUANITE, Xerxes Giah D.

PERUCHO, Queenie Jezreel A.SEMBRANO, Abigail T.

What is

ROTATIONAL

MOTION?

Rotational Motion- refers to motion of

a body about a fixed axis of rotation wherein, the particles have the same instantaneous angular velocity.

What is a

ROTATIONAL

INERTIA?

INTRODUCTIONRotational inertia, which is also termed

as moment of inertia, is a similar concept applied to objects whose motion is rotational instead of linear. The rotational inertia of an object is that object’s resistance to a change in its angular velocity. That is, if an object is spinning, it has a tendency to keep spinning until a net torque acts upon it.

FORMULAFor the very special case of the

moment of inertia of a single mass m, rotating about an axis, a distance r from m, we have

I=mr2

Figure Axis FormulaThin ring Axis through

centerI=mr2

Disk Axis through center

I=½ mr2

Thin rod Axis through one end

perpendicular to length

I=1/3 ml2

Sample ProblemFind the moment of inertia of a

solid cylinder of mass 3.0 kg and radius 0.50 m, which is free to rotate about an axis through its center.

Given: m = 3.0 kg r = 0.50 m

Find: I

Solution:I = ½ mr2

= ½ (3.0 kg) (0.50 m)2

= ½ (3.0 kg) (0.25m2) = 0.38 kg m2

Laws for Rotational Motion

1st law for rotational motion:A body in motion at a constant

angular velocity will continue in motion at that same angular velocity, unless acted upon by some unbalanced external torque.

2nd law for rotational motion:When an unbalanced external

torque acts on a body with moment of inertia I, it gives that body an angular acceleration a, which is directly proportional to the torque T and inversely proportional to the moment of inertia.

3rd law for rotational motion:If body A and body B have the

same axis of rotation, and if body A exerts a torque on body B, then body B exerts an equal but opposite torque on body A.

What is

TORQUE?

Torque is the quantity that measures how effectively a force (F) causes acceleration.

a train wheelThe magnitude of the torque can be calculated by:

T= F x l

Sample Problem The width of a door is 40 cm. If it is opened by

applying a force of 2 N at its edge (away from the hinges), calculate the torque produced which causes the door to open.

Solution : Length of lever arm = 40 cm = 0.40 m (since distance between axis of rotation and line of action of force is 40 cm)Force applied = 2 NTorque = Lever arm x force applied           = 0.40 x 20           = 8 Nm (8 Newton meter)

What is

the

CENTER

OF

GRAVITY?

The center of gravity is the point from where all the weight of an object is said to be concentrated.

Locating the Center of Gravity

A system is provided for determining the center of gravity of a body by providing a balance arm supported from a single pivot point, then positioning the body on the balance arm and measuring the rotation of the balance arm in two orthogonal planes.

What is

STABILITY

?

What is

CENTRIPETA

L FORCE?

We have just seen that a body in uniform circular motion experiences a centripetal acceleration. From Newton’s second law of motion, there must be a force that gives an object this acceleration.

Applying Newton’s Second Law to an object in uniform circular motion,

F = maFc = mac

= mv2

r Fc = mv2

r

Sample ProblemsA 400-g rock attached to a 1.0 m string is whirled

in a horizontal circle at the constant speed of 10.0 m/s. Neglecting the effects of gravity, what is the centripetal force acting on the rock?

Given: v = 10.0 m/s r = 1.0 m m = 400 g x 1kg = 0.4 kg 1000 g Find: Fc

Solution: Fc = mv2

r = (0.4 kg) (100 m2/s2)

m = 40 kg ∙ m/s2

= 40 N

What is

CENTRIFUGA

L FORCE?

An object traveling in a circle behaves as if it is experiencing an outward force. This force known as the centrifugal force.

Fc = mv2/r, where Fc =

centrifugal force, m = mass, v = speed,

and r =

radius. 

What is

SIMULATE

D

GRAVITY?

Simulated gravity is the varying (increase or decrease) of apparent gravity (g-force) via artificial means, particularly in space, but also on the Earth.

What is

ANGULAR

MOMENTU

M?

An angular momentum is the property characterizing the rotary inertia of an object or system of objects in motion about an axis that may or may not pass through the object or system. Angular momentum is a vector quantity, requiring the specification of both a magnitude and a direction for its complete description.

H = I ω H = angular momentum 

I = inertia  w = inertial space

Conservation of Angular Momentum

    Momentum is the product of inertia and velocity.  Inertia means the tendency of something not to change, and velocity means how fast it moves.  So momentum means the tendency of an object in motion not to slow down.  Momentum is of two kinds, angular and linear.  Both kinds of momentum are conserved in any collision.  Conservation means that none is lost, so the total momentum of the system before the collision, plus any additional impulse from outside the system, will equal the total momentum after the collision.  This conservation principle is key to deriving formulas.

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