Chapter 8

Part complete Calculate the tension in a horizontal string that whirls a 1.5-kg toy in a circle of radius 2.1 m when it moves at 3.1 m/s on an icy surface. Centripetal Force: F=mv2/r

F = 6.9 N

tangential speed

Linear speed along a curved path.

The net force exerted on a car traveling in a circular path at constant speed is

directed toward the center of the curve.

Your pet hamster sits on a record player that has constant angular speed. If the hamster moves to a point twice as far from the center, then its linear speed

doubles

The tangential speed on the outer edge of a rotating carousel is _______.

greater than toward the center

Where is the center of mass of a hollow soccer ball?

in the center of the ball

To tighten a bolt, you push with a force of 72 N at the end of a wrench handle that is 0.30 m from the axis of the bolt. What torque are you exerting? If you move your hand inward to be only 0.10 m from the bolt, find the force that you should exert to achieve the same torque. Do your answers depend on the direction of your push relative to the direction of the wrench handle?

τ = 22 N⋅m F = 220 N yes

Calculate the torque produced by a 54-N force when a pipe extends the length of the wrench to 0.56 m . Torque = Lever Arm × Force

τ = 30 N⋅m

Part complete If a trapeze artist rotates once each second while sailing through the air and contracts to reduce her rotational inertia to one-third of what it was, how many rotations per second will result?

ω = 3.00 rotations per second

A 1-kg rock is suspended from the tip of a horizontal meterstick at the 0-cm mark so that the meterstick barely balances like a seesaw when its fulcrum is at the 25-cm mark. From this information, the mass of the meterstick is

1 kg

On a balanced seesaw, a boy three times as heavy as his partner sits

1/3 the distance from the fulcrum.

A flywheel's diameter is twice that of another of the same shape and mass. Rotational inertia of the larger flywheel is

4x greater

centripetal force

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

centrifugal force

An apparent outward force on a rotating or revolving body.

If a skater who is spinning pulls her arms in so as to reduce her rotational inertia by half, by how much will her angular momentum change? By how much will her rate of spin change?

Her angular momentum does not change. Her spin rate doubles.

What is meant by the "lever arm" of a torque?

It is the perpendicular distance from the rotational axis to the line along which the force acts.

A person having a mass of 95 kg sits on the edge of a horizontal rotating platform, 2.5 m from the center of the platform, and has a tangential speed of 7.0 m/s. Calculate the angular momentum of the person. Angular Momentum = mvr

L = 1700 kg⋅m^2 / s

rotational inertia

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

If you hang at rest by your hands from a long vertical rope, where is your center of gravity with respect to the rope?

Somewhere straight below where your hands grab the rope

Dan and Sue cycle at the same speed. The tires on Dan's bike are larger in diameter than those on Sue's bike. Which wheels, if either, have the greater rotational speed?

Sue's

On a rotating turntable, how do tangential speed and rotational speed vary with distance from the center?

Tangential speed increases with distance. Rotational speed is constant.

Inertia depends on mass; rotational inertia depends on mass and something else. What?

The distribution of mass about the axis of rotation

rotational speed

The number of rotations or revolutions per unit of time; often measured in rotations or revolutions per second or minute.

center of gravity (cg)

The point at the center of an object's weight distribution where the force of gravity can be considered to act.

angular momentum

The product of a body's rotational inertia and rotational velocity about a particular axis. For an object that is small compared with the radial distance, its magnitude is the product of mass, speed, and radial distance from the spin axis. Angular momentum = mvr

torque

The product of force and the lever-arm distance, which tends to produce rotational acceleration. Torque = lever-arm distance × force

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.)

Which will have the greater acceleration rolling down an incline: a hoop or a solid disk? Why?

The solid disk will because the mass is closer to the axis of rotation.

If you are not wearing a seat belt in a car that rounds a curve, and you slide across your seat and slam against a car door, what kind of force is responsible for your slide: centripetal, centrifugal, or no force?

There is no force as viewed by someone outside the car. To them you move in a straight line.

What does a torque tend to do to an object?

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

When you whirl a can at the end of a string in a circular path, what is the direction of the force you exert on the can?

Toward the center of the circle

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.

The rock and meterstick balance at the 25-cm mark, as shown. The meterstick has a mass of 0.90 kg . (Figure 1) What must be the mass of the rock?

m = 0.90 kg

Horses with the greatest linear speed on a merry-go-round are located

near the outside

As a huge rotating cloud of particles in space gravitate together forming an increasingly dense ball, it shrinks in size and

rotates faster

A torque acting on an object tends to produce

rotation

The rotational inertia of your leg is greater when your leg is

straight

Which jar will roll down an incline in the shortest time, an empty one or one filled with peanut butter?

the filled jar