Physics 105 Chater 8 Rotational Motion

Centripetal force

A center-directed force that causes an object to follow a curved or circular path.

If a spinning skater pulls her arms in so as to reduce her rotational inertia by half, by how much will her rate of spin increase?

Angular momentum remains the same, while her rate of spin doubles.

Where is the center of gravity of the broom that Dr. Hewitt holds up?

At the Balance point

Centrifugal force

Center Fleeing or away from center

Any rotating system, your tangential speed depends on___________?

How far you are from the axis of rotation

A girl spins around in a circle trying to make herself dizzy. Without changing her position, she starts spinning twice as fast. By how much did her rotational kinetic energy change?

It quadrupled. Explanation: It must quadruple because rotational kinetic energy is given by the equation Krot���� = 12Iω212��2.

When the mass is farther from the axis of rotation the moment of inertia is?

Larger

Can a centripetal force sometimes act in a direction away from the center of rotation?

No. Such a force would be called centrifugal.

Impulse

Product of force and the time interval during which the force acts. Impulse produces change in momentum.

Which varies with radial distance on a rotating turntable, tangential speed or rotational speed?

Tangential speed increases with distance. Rotational speed is constant.

Tangential speeds and linear speeds are related_____

Tangential speed is directly proportional to rotational speed at any fixed distance from the axis of rotation.

Precesssion

The Earth wobbles on its axes changing the point in the year at which the Earth is closest to the sun over 21,000 year time cycle.

Folcrum

The fixed point around which a lever pivots

When Dr. Hewitt cuts the broom right through the center of gravity, how do the weights of the two sides of the broom compare?

The shorter side, where the bristles of the broom are, has a greater weight than the handle.

How does the torque due to the weight of one side of the broom exerted around the balance point compare with the torque exerted by the weight of the other side of the broom around the balance point?

The torque due to the weight of the shorter side (the bristles of the broom) is equal in magnitude to the torque due to the weight of the longer side, and opposite in direction.

Is it an inward force or an outward force that is exerted on the clothes during the spin cycle of a washing machine?

The tub of the machine exerts centripetal inward force on clothes.

Predict how the upward force exerted on the feet by the scale will compare to the weight of the man if the elevator is moving upward at a constant speed.

The upward force on the feet will be equal to the man's weight. Submit Newtons nd law

conservation of angular momentum.

When no external torque acts on an object or a system of objects, no change of angular momentum can occur. Hence, the angular momentum before an event involving only internal torques or no torques is equal to the angular momentum after the event.

If something moves other than in a non-straight-line path, can we say for sure that a net force acts on it?

Yes, for sure. That's the law, Newton's first!

To double the rotational speed the centripetal force must

be four times larger

Centripetal means

center seeking

Centripetal force is

directly proportional to the square of the rotational speed (angular velocity).

linear speed

distance traveled per unit of time

When a rock tied to a string whirled in a horizontal circle somehow doubles in mass but keeps the same speed, the string tension

doubles

Consider someone in a rotating space habitat. The outward force felt by the person

has no reaction counterpart

Tangential speed unlike rotational speed depends on________

radial distance (distance from the axis)

If no external net torque acts on a rotating system, the angular momentum of that system______?

remains constant.

Calculate the torque produced by a 56-NN perpendicular force at the end of a 0.15-mm-long wrench.

t=8.4 N*m

rotational speed

the number of rotations or revolutions per unit of time

The angular momentum of our solar system nicely remains the same century after century. What would be needed for it to be altered?

A force external to our solar system would be the culprit. No force internal to the solar system could do it!

Why doesn't the LEaning Tower of Pisa topple over?

A vertical line through the center of gravity passes inside its support base.

Suppose we replace both hover pucks with pucks that are the same size as the originals but twice as massive. Otherwise, we keep the experiment the same. Compared to the pucks in the video, this pair of pucks will rotate

At the same rate Explanation: Due to the conservation of angular momentum, the angular momentum of the two-puck system before and after the collision is equal. Since the relationship between the moment of inertia and mass is linear (i.e. (I� α� mm), by doubling the mass, we double the moment of inertia. However, the moment of inertia both before and after the collision increases by the same factor of 2, so this impact ends up canceling out. Therefore, since the velocity before the collision is kept unchanged, the final rate of rotation will remain the same as well.

A baseball bat can be rotated around many different axes of rotation. Three such possibilities are shown in (Figure 1). Rank the baseball bat's moment of inertia about each of these three axes of rotation.

B-A-C Explanation:Because the total mass is the same for all three axes, only the distribution of that mass changes the moment of inertia. All of the mass is close to axis C, so that the axis has the smallest moment of inertia. The bulk of the mass (in the meat of the bat) is further from axis B than A; therefore, axis B has the largest moment of inertia.

Why is it easier to remove an old bolt if we add an extension to the wrench handle?

Because a higher torque is applied

Why is it easier to tear a piece of toilet paper form a larger toilet paper roll than a smaller roll?

Because the larger roll has a greater mass and a larger radius so it so it moment of inertia is greater than the smaller roll.

A flea sits on a rotating turntable, midway from the center to the edge. A second flea sits at the edge. Which flea has the higher ? Which has the higher v?

Both fleas rotate at the same rpm, . The flea at the edge has twice the tangential speed v.

Given the same baseball bat and possible axes of rotation shown in (Figure 1), for which axis of rotation would it be the easiest to rotate the bat from rest?

C The smaller the moment of inertia of an object, the easier it is to change its state of rotation.

Moment of inertia to an object's mass and shape

Depends both on its mass and how that mass is distrubuted. having more mass and putting that mass farther away from the rotation axis increases the objects moment of inertia.

What is required to change the angular momentum of a system?

External torque

The torque exerted by a crowbar on an object increases with increased?

Force and distance

Newton's Second Law

Force equals mass times acceleration

The experimenter from the video rotates on his stool, this time holding his empty hands in his lap. You stand on a desk above him and drop a long, heavy bean bag straight down so that it lands across his lap, in his hands. What happens?

He spins slower explanation:The bean bag is not rotating before it contacts the experimenter, so (by conservation of rotational momentum) he must supply the rotational momentum required to make it spin at the same rate as his lap. Therefore, he ends up spinning slower.

tangential speed

Linear speed along a curved path

How does moment of interia relate to an objects rotation?

Moment of inertia determines an object's resistance to changing it's rotational motion

angular momentum

Product of rotational inertia and rotational velocity

Rotational inertia

Reluctance or apparent resistance of an object to change its state of rotation, is determined by the distribution of the mass of the object and the location of the axis of rotation or revolution.

rotational velocity

Rotational speed together with a direction for the axis of rotation or revolution

when most of the mass is closer to the axis of rotation the moment of inertis is?

Smaller

A solid sphere and a hollow sphere (spherical shell) of the same mass and same radius rotate with the same amount of kinetic energy. Which one is rotating faster?

The Solid Sphere Explanation: ecause the rotational kinetic energy is given by the equation Krot���� = 12Iω212��2, the object with the smaller moment of inertia would have to spin faster to obtain the same value for the rotational kinetic energy. The hollow sphere is just like the solid sphere, except that you would take the mass near the axis for the solid sphere and shove it outwards towards the surface. Moving mass further from the axis of rotation makes the moment of inertia for the hollow sphere larger than the solid sphere.]

The moment of interia depends on

The mass of the object also its shape and distribution of the mass throughout that shape. I=Emr^2

linear momentum

The product of the mass and the velocity of an object; also called momentum. (This definition applies at speeds much lower than the speed of light.

Torque

The product of this lever arm and the force that tends to produce rotation.

What kind of motion does a torque tend to impart on an object?

Torque tends to twist or change the state of rotation of the object.

Torque

a force that causes rotation

Why is tangential speed expressed and not v=rw?

angential speed is expressed as the proportion because the units of v and don't match. If is expressed in units of radians/second, then units match and the proportion becomes the exact equation . To prevent "information overload" (this author's nemesis) we'll forgo a radian treatment and refer the reader to the footnotes at the bottom of the preceding page.

angular momentum- an object or system of objects will maintain it's angular momentum unless acted upon by an external net torque

angular momentum=mvr

Circular Motion

any motion in which an object is moving along a curved path

The center of gravity of a basketball is located where?

at its geometrical center Submit

What if the object is already rotating, would a moving merrygo round be harder to stop if a). there were no children on it b). if there were chilrdern standing near the center c). or if ther were children standing near the edge?

children standing near the edge Explanation: the larger moment of inertia of the merry go round system the more difficult it will be to slow it down to a stop, by adding mass far away from the axis of rotation the moment of inertia of the mery go round system is increased.

kinetic energy of a child spining

cnter of mass isn't moving, sothe kinetic eneryg formula would give and answer of zero. However when something is moving there is kinetic energy associated with that motion. kinetic engery due to rotation is called Rotational kinetic energy.

A car skids on a curve when the centripetal force (friction of road on tires) ____?

is not great enough.

The rotational speed of every point of a rotating rigid object _______.

is the same

Anything that moves in a circular path does so because______?

it's acted upon by a centripetal force.

To improve the performance of a racing bicycle, the mass of the tires and rims is reduced so there is____________

less rotational inertia

We are familiar with the units of linear speed: or . What are the units of tangential speed?

m/s or km/h

Rotational motion

motion of a body that spins about an axis

A ruler is in equilibrium on the tip of your finger only if_____

net torque and net force are zero

When a rock tied to a string is whirled in a horizontal circle, doubling the speed _______

quadruples the tension in the string

Tangential speed~radial distance*rotational speed

v~rw

What are the units of rotational speed w ?

we express rotational speed in familiar rotations per minute (rpm). More generally, is the rate at which angles expressed in radians are swept out per second.