ConcepTest 9.4ConcepTest 9.4 Using a WrenchUsing a Wrench

You are using a wrench to

loosen a rusty nut. Which

arrangement will be the

most effective in loosening

the nut?

1

34

2

5) all are equally effective

ConcepTest 9.4ConcepTest 9.4 Using a WrenchUsing a Wrench

You are using a wrench to

loosen a rusty nut. Which

arrangement will be the

most effective in loosening

the nut?

1

34

2

Since the forces are all the same, the only difference is the lever arm. The arrangement with the largest largest

lever armlever arm (case #2case #2) will

provide the largest torquelargest torque.

5) all are equally effective

Follow-up:Follow-up: What is the difference between arrangement 1 and 4? What is the difference between arrangement 1 and 4?

ConcepTest 9.6ConcepTest 9.6 Closing a DoorClosing a Door

In which of the cases shown below

is the torque provided by the

applied force about the rotation

axis biggest? For all cases the

magnitude of the applied force is

the same.

1) F1

2) F3

3) F4

4) all of them

5) none of them

ConcepTest 9.6ConcepTest 9.6 Closing a DoorClosing a Door

1) F1

2) F3

3) F4

4) all of them

5) none of them

In which of the cases shown below

is the torque provided by the

applied force about the rotation

axis biggest? For all cases the

magnitude of the applied force is

the same.

The torque is: == F d sin F d sin

and so the force that is at 90°90°

to the lever arm is the one that

will have the largest torquelargest torque.

Clearly, to close the door, you

want to push perpendicularperpendicular!!

Follow-up:Follow-up: How large would the force have to be for How large would the force have to be for FF44??

ConcepTest 9.8aConcepTest 9.8a Dumbbell IDumbbell I

1) case (a)1) case (a)

2) case (b)2) case (b)

3) no difference3) no difference

4) It depends on the rotational 4) It depends on the rotational inertia of the dumbbell.inertia of the dumbbell.

A force is applied to a dumbbell for a certain period of time, first as in (a) and then as in (b). In which case does the dumbbell acquire the greater center-of-mass speed ?

ConcepTest 9.8aConcepTest 9.8a Dumbbell IDumbbell I

1) case (a)1) case (a)

2) case (b)2) case (b)

3) no difference3) no difference

4) It depends on the rotational 4) It depends on the rotational inertia of the dumbbell.inertia of the dumbbell.

A force is applied to a dumbbell for a certain period of time, first as in (a) and then as in (b). In which case does the dumbbell acquire the greater center-of-mass speed ?

Because the same force acts for the

same time interval in both cases, the

change in momentum must be the

same, thus the CM velocity must be

the same.

1) case (a)1) case (a)

2) case (b)2) case (b)

3) no difference3) no difference

4) It depends on the rotational 4) It depends on the rotational inertia of the dumbbell.inertia of the dumbbell.

A force is applied to a dumbbell for a certain period of time, first as in (a) and then as in (b). In which case does the dumbbell acquire the greater energy ?

ConcepTest 9.8bConcepTest 9.8b Dumbbell IIDumbbell II

1) case (a)1) case (a)

2) case (b)2) case (b)

3) no difference3) no difference

4) It depends on the rotational 4) It depends on the rotational inertia of the dumbbell.inertia of the dumbbell.

A force is applied to a dumbbell for a certain period of time, first as in (a) and then as in (b). In which case does the dumbbell acquire the greater energy ?

If the CM velocities are the same,

the translational kinetic energies

must be the same. Because

dumbbell (b) is also rotating, it has

rotational kinetic energy in addition.

ConcepTest 9.8bConcepTest 9.8b Dumbbell IIDumbbell II

ConcepTest 9.9ConcepTest 9.9 Moment of InertiaMoment of Inertia

1) 1) solid aluminum

2) hollow gold2) hollow gold

3) same3) same

same mass & radius

solid hollow

Two spheres have the same radius and equal masses. One is made of solid aluminum, and the other is made from a hollow shell of gold.

Which one has the bigger moment of inertia about an axis through its center?

ConcepTest 9.9ConcepTest 9.9 Moment of InertiaMoment of Inertia

1) 1) solid aluminum

2) hollow gold2) hollow gold

3) same3) same

same mass & radius

solid hollow

Two spheres have the same radius and equal masses. One is made of solid aluminum, and the other is made from a hollow shell of gold.

Which one has the bigger moment of inertia about an axis through its center?

Moment of inertia depends on mass and distance from axis squared. It is bigger for the shell since its mass is located

farther from the center.

ConcepTest 9.10ConcepTest 9.10 Figure SkaterFigure Skater

1) the same1) the same

2) larger because she’s rotating 2) larger because she’s rotating fasterfaster

3) smaller because her rotational 3) smaller because her rotational

inertia is smallerinertia is smaller

A figure skater spins with her arms extended. When she pulls in her arms, she reduces her rotational inertia and spins faster so that her angular momentum is conserved. Compared to her initial rotational kinetic energy, her rotational kinetic energy after she pulls in her arms must be

ConcepTest 9.10ConcepTest 9.10 Figure SkaterFigure Skater

1) the same1) the same

2) larger because she’s rotating 2) larger because she’s rotating fasterfaster

3) smaller because her rotational 3) smaller because her rotational

inertia is smallerinertia is smaller

A figure skater spins with her arms extended. When she pulls in her arms, she reduces her rotational inertia and spins faster so that her angular momentum is conserved. Compared to her initial rotational kinetic energy, her rotational kinetic energy after she pulls in her arms must be

KErot=1/2 I 2 = 1/2 L (used L= I ).

Since L is conserved, larger

means larger KErot. The “extra”

energy comes from the work she

does on her arms.

Follow-up:Follow-up: Where does the extra energy come from? Where does the extra energy come from?

ConcepTest 9.12 ConcepTest 9.12 Spinning Bicycle WheelSpinning Bicycle Wheel

You are holding a spinning bicycle wheel while standing on a stationary turntable. If you suddenly flip the wheel over so that it is spinning in the opposite direction, the turntable will

1) remain stationary1) remain stationary

2) spin in the same direction as the 2) spin in the same direction as the wheel before flippingwheel before flipping

3) spin in the same direction as the 3) spin in the same direction as the wheel after flippingwheel after flipping

ConcepTest 9.12 ConcepTest 9.12 Spinning Bicycle WheelSpinning Bicycle Wheel

You are holding a spinning bicycle wheel while standing on a stationary turntable. If you suddenly flip the wheel over so that it is spinning in the opposite direction, the turntable will

The total angular momentum of the system is L upward, and it is conserved. So if the wheel has -L downward, you and the table must have +2L upward.

1) remain stationary1) remain stationary

2) spin in the same direction as 2) spin in the same direction as the wheel before flippingthe wheel before flipping

3) spin in the same direction as 3) spin in the same direction as the wheel after flippingthe wheel after flipping

ConcepTest 11.1ConcepTest 11.1 Balancing RodBalancing Rod

1kg

1m

A 1 kg ball is hung at the end of a rod 1

m long. If the system balances at a

point on the rod 0.25 m from the end

holding the mass, what is the mass of

the rod ?

1) 1/4 kg

2) 1/2 kg

3) 1 kg

4) 2 kg

5) 4 kg

1 kg

X

CM of rod

same distance mROD = 1 kg

A 1 kg ball is hung at the end of a rod 1

m long. If the system balances at a

point on the rod 0.25 m from the end

holding the mass, what is the mass of

the rod ?

The total torque about the The total torque about the

pivot must be zero !!pivot must be zero !! The CM

of the rod is at its center, 0.25 0.25

m to the right of the pivotm to the right of the pivot.

Since this must balance the

ball, which is the same distance same distance

to the left of the pivotto the left of the pivot, the

masses must be the same !!

1) 1/4 kg

2) 1/2 kg

3) 1 kg

4) 2 kg

5) 4 kg

ConcepTest 11.1ConcepTest 11.1 Balancing RodBalancing Rod

ConcepTest 11.2ConcepTest 11.2 MobileMobile

1 kg

1 m 3 m

1 m 2 m

?

?

A (static) mobile hangs as shown

below. The rods are massless and

have lengths as indicated. The mass

of the ball at the bottom right is 1 kg.

What is the total mass of the mobile ?

1) 5 kg

2) 6 kg

3) 7 kg

4) 8 kg

5) 9 kg

1 kg

1 m 3 m

1 m 2 m

?

?

A (static) mobile hangs as shown

below. The rods are massless and

have lengths as indicated. The mass

of the ball at the bottom right is 1 kg.

What is the total mass of the mobile ?

1) 5 kg

2) 6 kg

3) 7 kg

4) 8 kg

5) 9 kg

Use torques in two steps: (1)

find the big mass on the bottom

left (lower rod only). (2) use the

entire lower rod assembly (with

two masses) to find the mass on

top right. Finally, add up all the Finally, add up all the

masses.masses.

ConcepTest 11.2ConcepTest 11.2 MobileMobile

ConcepTest 11.3aConcepTest 11.3a Tipping Over ITipping Over I

1 2 3

1) all

2) 1 only

3) 2 only

4) 3 only

5) 2 and 3

A box is placed on a ramp in the

configurations shown below. Friction

prevents it from sliding. The center of

mass of the box is indicated by a blue

dot in each case. In which case(s) does

the box tip over ?

ConcepTest 11.3aConcepTest 11.3a Tipping Over ITipping Over I

1 2 3

1) all

2) 1 only

3) 2 only

4) 3 only

5) 2 and 3

A box is placed on a ramp in the

configurations shown below. Friction

prevents it from sliding. The center of

mass of the box is indicated by a blue

dot in each case. In which case(s) does

the box tip over ?

The torque due to gravity acts like all

the mass of an object is concentrated

at the CM. Consider the bottom right

corner of the box to be a pivot point.

If the box can rotate such that the CM If the box can rotate such that the CM

is lowered, it will !!is lowered, it will !!

ConcepTest 11.3bConcepTest 11.3b Tipping Over IITipping Over II

1) case 1 will tip

2) case 2 will tip

3) both will tip

4) neither will tip

Consider the two configurations of

books shown below. Which of the

following is true?

1/2

1/4 1/2

1/4

1 2

ConcepTest 11.3bConcepTest 11.3b Tipping Over IITipping Over II

The CM of the system is

midway between the CM of

each book. Therefore, the

CM of case #1 is not over the CM of case #1 is not over the

table, so it will tiptable, so it will tip.

1) case 1 will tip

2) case 2 will tip

3) both will tip

4) neither will tip

Consider the two configurations of

books shown below. Which of the

following is true?

1/2

1/4 1/2

1/4

1 2