Q: A box is resting on a level surface and not moving. Which of the following is true about the forces acting on the box?

$$\sum \vec{F} = 0$$ and $$\sum \tau = 0$$

Q: Which of the following conditions must be satisfied for an object to be in static equilibrium?

$$\sum \vec{F} = 0$$ and $$\sum \tau = 0$$

Q: A disk on a frictionless floor is acted on by three forces: $$F$$, $$2F$$, and $$3F at $$different points. Which condition must be met for the disk to be in equilibrium?

$$\sum \vec{F} = 0$$ and $$\sum \tau = 0$$

Question 1

An ice skater with arms extended has a moment of inertia $$I_i = 4.0\ \mathrm{kg\ m^2$}$$ and is spinning at an angular velocity $$\omega_i = 2.0\ \mathrm{rad/s}. $$After pulling in her arms, her moment of inertia decreases to $$I_f = 1.0\ \mathrm{kg\ m^2$}. $$What is her new angular velocity $$\omega_f$$ after pulling in her arms?

Accepted Answer

$$\omega_f = 8.0\ \mathrm{rad/s}$$

Question 2

If the skater's initial rotational kinetic energy is $$KE_{rot,i}$$, what is her final rotational kinetic energy $$KE_{rot,f}$$ after pulling in her arms?

Accepted Answer

$$KE_{rot,f} = 32\ \mathrm{J}$$

Question 3

Which physical principle explains why the skater's angular velocity increases when she pulls her arms in?

Accepted Answer

Conservation of angular momentum

Question 4

A steel beam is lifted by a crane at constant speed. Which type of equilibrium is the beam experiencing?

Accepted Answer

Dynamic equilibrium

Question 5

A box is resting on a level surface and not moving. Which of the following is true about the forces acting on the box?

Accepted Answer

$$\sum \vec{F} = 0$$ and $$\sum 	au = 0$$

Question 6

A jet plane has just reached cruising speed and altitude. What type of equilibrium is it in?

Accepted Answer

Dynamic equilibrium

Question 7

Which of the following conditions must be satisfied for an object to be in static equilibrium?

Accepted Answer

$$\sum \vec{F} = 0$$ and $$\sum 	au = 0$$

Question 8

A figure skater increases her rotational kinetic energy by pulling in her arms. What is the source of this increase in kinetic energy?

Accepted Answer

Work done by internal forces (muscles)

Question 9

A disk on a frictionless floor is acted on by three forces: $$F$$, $$2F$$, and $$3F at $$different points. Which condition must be met for the disk to be in equilibrium?

Accepted Answer

$$\sum \vec{F} = 0$$ and $$\sum 	au = 0$$

Question 10

If a steel beam is slowing down as it is lifted by a crane, what type of equilibrium is it experiencing?

Accepted Answer

Not in equilibrium

Question 11

A $$1.0\ \mathrm{kg\ m^2$}$$ disk is spinning at $$8.0\ \mathrm{rad/s}. $$What is its rotational kinetic energy?

Accepted Answer

$$32\ \mathrm{J}$$

Question 12

Which of the following best describes dynamic equilibrium?

Accepted Answer

The object moves at constant velocity and all forces and torques sum to zero.

Question 13

A $$4.0\ \mathrm{kg\ m^2$}$$ skater spinning at $$2.0\ \mathrm{rad/s}$$ pulls in her arms, reducing her moment of inertia to $$1.0\ \mathrm{kg\ m^2$}. $$What is her final rotational kinetic energy?

Accepted Answer

$$32\ \mathrm{J}$$

Question 14

Which of the following is NOT a requirement for static equilibrium?

Accepted Answer

The object must be moving at constant velocity.

Question 15

A box is pushed and starts sliding across the floor at constant speed. What type of equilibrium is it in?

Accepted Answer

Dynamic equilibrium

Question 16

If the sum of the forces on an object is zero but the sum of the torques is not zero, what will happen?

Accepted Answer

The object will rotate.

Question 17

A $$2.0\ \mathrm{kg\ m^2$}$$ disk is spinning at $$4.0\ \mathrm{rad/s}. $$What is its rotational kinetic energy?

Accepted Answer

$$16\ \mathrm{J}$$

Question 18

Which of the following scenarios is NOT in equilibrium?

Accepted Answer

A beam slowing down as it is lifted

Question 19

If a system is in static equilibrium, which of the following must be true?

Accepted Answer

The system is at rest and $$\sum \vec{F} = 0$$ and $$\sum 	au = 0$$

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