Second: Use the acceleration to find the force acting on the ball, and then remember that the change in Kinetic Energy equals the net work done on it (W = F∆x). (Don’t worry about initial because it starts at rest)

ANS: 864 J

ANS: [20]i + [-30] j kg/m*s

What is the initial momentum pi of the ball?

ANS: [0]i + [-10] j kg/m*s

What is the impulse or change in momentum ∆p of the ball?

ANS: [20]i + [-40] j kg/m*s

What is the final momentum pf of the ball?

ANS: (400 + 900)/2*1 ==> 650 J

What is the initial kinetic energy Ki of the ball?

ANS: (400 + 1600)/2*1 ==> 1000 J

What is the final kinetic energy Kf of the ball?

ANS: 1000 J – 650 J = 350 J

What is the change in kinetic energy ∆K of the ball?

ANS: 350J = (-10) * ∆y ==> ∆y = -35 m

What is the ball’s change in height ∆y after it falls 1 s?

ANS: (0.5*40m/s) = (0.5*-8m/s)+(2*V₂f) ==> V₂f = 12 m/s

What is the final velocity, V₂f, of puck 2 after the collision?

ANS: UP

What is the direction of the angular velocity vector?

ANS: DOWN

ANS: ω = 2 + (-2 * 4s) ==> -6 rad/s

ANS: ?

ANS: (.1m * – 6 rad/s) ==> -.6 m/s

ANS: (.1m * -2 rad/s²) ==> -.2 m/s²

Incorrect: F2 = F1/4

Incorrect: F2 = 16 F1

Correct: None of the above.

Correct: τ₂ = 16 τ₁

Incorrect: τ₂ = 4 τ ₁

Incorrect: τ₂ = τ¼

Correct: F₂ = 28 F₁

Incorrect: F₂ = 16 F₁

Incorrect: F₂ = 49 F₁

Incorrect: τ2 = 49 τ1

Incorrect: τ2 = 4 τ1

Incorrect: τ2 = 28 τ1

What is the resulting torque in terms of RT?

[Remember to check whether the torque is positive (results in CCW motion) or negative (results in CW motion). ]

ANS: 1 RT

A rope of tension 1T applies a force at radius 3R on the spool. It is located at 9 o’clock and points upward.

What is the resulting torque in terms of RT?

ANS: -3 RT

In the following questions, the spool is pulled by tension forces that are applied at various locations, directions, and radii.

To solve each problem, draw the spool as a circle on a piece of paper and then draw the given tension vectors.

REMEMBER that the direction UPWARD points to the TOP of the page and DOWNWARD points to the BOTTOM of the page.

The resulting TORQUE will be either OUT OF the page (CCW motion, POSITIVE torque) or INTO the page (CW motion, NEGATIVE torque).

DISK = ½

SOLID SPHERE = 2/5

I disk = 8 MR²

What are the moments of inertia for the ring and disk? Write your answer in terms of MR²

Remember to use Coefficients of Inertia

What is the initial angular momentum for the ring? Write your answer in terms of MR²ω.

Remember to use Coefficients of Inertia

What is the initial angular momentum for the disk? Write your answer in terms of MR²ω.

Remember that Li = Iω, where I is the moment of inertia of the disk and ω is the angular velocity of the disk. Also, the CW motion of the disk gives a negative angular momentum value.

Remember to use Coefficients of Inertia

What is the initial angular momentum Li(ring+disk) of the system?

Remember to use Coefficients of Inertia

What is the final angular velocity ωf of the ring+disk system? Write your answer in terms of ω.

Remember that Li(ring+disk) = Lf(ring+disk) = If(ring+disk) ωf and solve for ωf using information calculated above.

Remember to use Coefficients of Inertia

Incorrect: insufficient information

Incorrect: simulation 1

Correct: simulation 2

1) In which simulation is the net force on the falling mass larger?

Incorrect: simulation 2

Incorrect: same

Correct: simulation 1

2) In which simulation is the tension in the rope larger?

Incorrect: same torque

Incorrect: simulation 2

Incorrect: insufficient information

3) In which simulation is the torque applied to the pulley (by the rope tension) larger?

Incorrect: same moment of inertia

Correct: simulation 1

Incorrect: insufficient information

4) In which simulation is the moment of inertia of the pulley larger?

Incorrect: pulley 1

Incorrect: same net forc

For which pulley is the net force on the falling mass larger?

Correct: pulley 1

Incorrect: pulley 2

For which pulley is the tension in the rope (and therefore torque on the pulley) larger?

Incorrect: same net force

Correct: pulley 1

For which pulley is the moment of inertia larger?

Incorrect: Krot = 0.2 Ktrans

Incorrect: Krot = 0.8 Ktrans

Correct: Krot = 0.4 Ktrans

Incorrect: none of the above

Remember that the rotational kinetic energy Krot = β mv²/2 and the translational kinetic energy Ktrans = mv²/2. Therefore, Krot = β Ktrans.

Incorrect: Ktrans = 1.40 Ktot

Incorrect: Ktrans = 1.67 Ktot

Incorrect: Ktrans = 1.20 Ktot

Incorrect: none of the above

Remember that the total kinetic energy of the object is (1 + β) mv²/2.

Incorrect: ring 1 reaches the bottom first

Incorrect: insufficient information to determine

Incorrect: ring 2 reaches the bottom first

Incorrect: ring reaches the bottom first

Incorrect: insufficient information to determine

Incorrect: they reach the bottom at the same time

Correct: sphere reaches the bottom first

Incorrect: insufficient information to determine

Incorrect: ring reaches the bottom first

Incorrect: hollow sphere reaches the bottom first

Incorrect: insufficient information to determine

Correct: solid sphere reaches the bottom first

Incorrect: insufficient information to determine

Incorrect: ring 1 has the greater change in height

Incorrect: ring 2 has the greater change in height

Correct: ring has the greater change in height

Incorrect: cylinder has the greater change in height

Incorrect: insufficient information

Incorrect: they both have the same change in height

Incorrect: kg m/s

Correct: kg m2/s2 or N*m

Incorrect: kg m/s2

Incorrect: kg m/s

Incorrect: m/s

Incorrect: kg m2/s2

Incorrect: I increases

Incorrect: I remains constant

Based on this information which statement is true about the moment of inertia I for the system (girl + masses)?

Incorrect: upwards

Incorrect: downwards

Incorrect: radially outward

What is the direction of the force applied by her arms?

Correct: 180 degrees

Incorrect: 270 degrees

Incorrect: 90 degrees

Incorrect: 45 degrees

In the formula for the torque exerted on the masses by the girl (τ = r x F) what is the angle between the force vector F and the position r of the masses?

Correct: r F sin(θ)

Incorrect: r F

Incorrect: r F cos(θ)

Incorrect: The kinetic energy of the system decreases because the moment of inertia decreases.

Correct: There is no net external torque on the system.

Incorrect: The angular momentum of the system increases.

Which statement below is true?