Mastering Physics Ch 8

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.

A small space telescope at the end of a tether line of length L moves at linear speed v about a central space station. 1. What will be the linear speed of the telescope if the length of the line is reduced to 0.33 L? 2. If the initial linear speed of the telescope is 1.3m/s , what is its speed when pulled in to one-third its initial distance from the space station?

1. vnew = v/0.33 2. 3.9 m/s

To tighten a bolt, you push with a force of 84N at the end of a wrench handle that is 0.26m from the axis of the bolt. 1. What torque are you exerting? 2. 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. 3. Do your answers depend on the direction of your push relative to the direction of the wrench handle?

1. τ = 22 N⋅m 2. F= 220 N 3. Yes

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

1/3 the distance from the fulcrum.

Consider two flywheels of the same size and shape, but one with twice the mass. Rotational inertia of the more massive one is

2 times greater

You can safely stand on the overhanging end of a heavy plank that rests on a table. How much overhang depends on your mass and the mass of the plank. If you can stand on the end of a plank that overhangs the edge of the supporting table 1/5 its total length, how massive is the plank compared to your mass?

2/3

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

4 times greater

If you're on a Ferris wheel at a carnival, seated 10 m from the Ferris wheel's axis that makes a complete rotation each minute, your linear speed is

62.8 m/min.

Why can't you stand with your heels and back to a wall and then bend over to touch your toes and return to your stand-up position?

A vertical line through the center of gravity of your body is in front of the tips of your toes, which is outside your support base.

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

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

The famous Leaning Tower of Pisa doesn't topple over because its center of gravity is

Above a place of support

What is the law of inertia for rotating systems in terms of angular momentum?

Angular momentum does not change without an applied external torque.

Consider three axes of rotation for a pencil: along the lead, at right angles to the lead at the middle, and at right angles to the lead at one end. Rate the rotational inertias about each axis from smallest to largest.

Axis along the lead, through the center, through one end

You can swing your legs to and fro more frequently when your legs are

Bent

Which of these animals has a quicker stride? A. cat B. horse C. mouse D. giraffe

C

A coin and a ring roll down an incline at the same time. The one to first reach the bottom is the

Coin

Compared with a force, a torque involves A. distance from an axis of B. rotation. C. leverage. D. all the above

D

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

A tightrope walker more easily balances on a tight wire if her pole

Droops

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 12.5-cm mark. From this information, the mass of the meterstick is A. 1/4 kg. B. 1 kg. C. 3/4 kg. D. 1/2 kg. E. none of the above

E

Calculate the TENSION in a horizontal string that whirls a 2.0-kg toy in a circle of radius 2.8m when it moves at 3.5m/s on an icy surface. CENTRIPETAL FORCE: F=mv^2/r

F = 8.8 N

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.

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

In the center of the ball

When a twirling ice skater brings her arms inward, her rotational speed

Increases

As distance increases between most of the mass of an object and its center of rotation, how does rotational inertia change?

It increases

Calculate the angular momentum of the person if the force of friction that keeps a 85-kg person sitting on the edge of a horizontal rotating platform when the person sits 1.5m from the center of the platform and has a tangential speed of 1.2m/s .Angular Momentum = mvr

L = 150 kg⋅m^2/s

As the polar icecaps melt, the resulting water spreads over the entire Earth. This new mass distribution tends to make the length of a day

Longer

How is a flywheel constructed to maximize its rotational inertia?

Most of the mass is concentrated far from the axis.

A ball that gains speed as it rolls down a hill experiences a

Net torque and Net force

If the string that holds a whirling can in its circular path breaks, what kind of force causes it to move in a straight- line path: centripetal, centrifugal, or no force? What law of physics supports your answer?

No force; Newton's first law

Two people are balanced on a seesaw. If one person leans inward toward the center of the seesaw, that person's end of the seesaw tends to

Rise

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

Rotates faster

Centrifugal forces are an apparent reality to observers in a reference frame that is

Rotating

A torque acting on an object tends to produce

Rotation

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

A ring, a disk, and a solid sphere begin rolling down a hill together. Which reaches the bottom first?

Sphere

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

Straight

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.

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

The filled jar

You can safely stand on the overhanging end of a heavy plank that rests on a table. How much overhang depends on your mass and the plank's mass. If you can stand on the end of a plank that overhangs the edge of the supporting table 1/4 its total length, how massive is the plank compared to your mass?

The same

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.

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

Which tin can will roll down an incline in the shortest time, one filled with water or one filled with ice? (Hint: water 'slides' inside the can.)

With water

The rotational inertia of a pencil is greatest about an axis

about its end, like a pendulum.

If Earth had a pair of identical moons on opposite sides of the same circular orbit, the center of gravity of the double-moon-Earth system would be

at the center of the Earth.

Centripetal force does no work on a circularly-moving object because

centripetal force has no component in the direction of motion.

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

directed toward the center of the curve

Tangential speed increases with distance. Rotational speed is constant.

greater than toward the center

What are the units of measurement for tangential speed? For rotational speed?

m/s for tangential, RPM for rotational

The rock and meterstick balance at the 25-cm mark, as shown. The meterstick has a mass of 1.0kg . What must be the mass of the rock?

m= 1 kg

A solitary boy cannot balance on a seesaw with its fulcrum at its midpoint. If the fulcrum is moved to one-quarter the distance from the boy, balance is achieved when the weight of the boy is

more than the weight of the seesaw.

Which horse moves faster in m/s on a merry-go-round?

one near outer rail

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

quadruples the tension in the string

As you crawl toward the edge of a large freely-rotating horizontal turntable in a carnival funhouse, the angular momentum of you and the turntable

remains the same, but the revolutions per minute decrease.

The force responsible for a car moving steadily along a no-friction icy banked curve is due to

the radial component of the normal force.

To kick a football so it won't topple end over end, kick it so the force of impact extends

through its center of gravity.

To rotate a stubborn screw, it is best to use a screwdriver that has a

wide handle.

Calculate the torque produced by a 48-N perpendicular force at the end of a 0.22-m-long wrench. Torque = Lever Arm × Force

τ = 11 Nm