Q: Which condition must be satisfied for a rigid body to be in complete equilibrium?

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

Question 1

Which of the following correctly defines the torque $$	au$$ produced by a force $$\vec{F}$$ acting at a distance $$r$$ from a pivot, at an angle $$	heta to $$the lever arm?

Accepted Answer

$$	au = rF\sin(	heta)$$

Question 2

A uniform 8 m wide, 6 m tall box is hinged at the bottom left corner. If a force $$F is $$applied horizontally to the top left corner, what is the torque about the hinge due to $$F$$?

Accepted Answer

$$	au = 6F$$

Question 3

For torque calculations involving gravity, from which point does gravity act on a rigid body?

Accepted Answer

From the center of mass

Question 4

A 4 m long bar has three forces acting on it: $$F_1 = 20$$\,\mathrm{N}$$ at 10$$^\circ$$ at the right end, F_2$ = 30\,\mathrm{N} at$$ $$30^\circ at $$the midpoint, and $$F_3 = 25$$\,\mathrm{N}$$ at 45$$^\circ$$ at the left end. What is the net torque about the left end?

Accepted Answer

$$-38.0\,\mathrm{Nm}$$

Question 5

Which statement about the lever arm (moment arm) in torque calculations is correct?

Accepted Answer

It is the perpendicular distance from the axis of rotation to the line of force.

Question 6

A 50-kg person stands at the right end of a 3.0 m long diving board, which is held in static equilibrium by a support at the left end and another at 0.50 m from the left end. If the board is weightless, what is the force exerted by the support at the left end?

Accepted Answer

$$300\,\mathrm{N}$$ upward

Question 7

Which condition must be satisfied for a rigid body to be in complete equilibrium?

Accepted Answer

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

Question 8

A 10 m long, 20 kg ladder leans against a frictionless wall at $$60^\circ to $$the ground. What is the minimum coefficient of friction $$\mu$$ needed to prevent slipping?

Accepted Answer

$$\mu = 0.26$$

Question 9

Which of the following is the correct formula for the moment of inertia $$I of a $$rigid body consisting of discrete masses $$m_i at $$distances $$r_i$$ from the axis?

Accepted Answer

$$I = \sum m_i r_i^2$

Question 10

Which of the following statements about the moment of inertia is true?

Accepted Answer

It depends on both the mass and the distribution of mass relative to the axis of rotation.

Question 11

A disk of mass $$M$$ and radius $$R$$ can be spun about its center (like a wheel) or about its edge (like a coin). Which statement is correct about its moments of inertia $$I_{center}$$ and $$I_{edge}$$?

Accepted Answer

$$I_{center} \u003c I_{edge}$$

Question 12

Which equation correctly expresses the rotational kinetic energy $$K_{rot} of a $$rigid body?

Accepted Answer

$$K_{rot} = \frac{1}{2} I \$$omega^2$$

Question 13

If multiple forces act on a rigid body, how is the net torque $$	au_{net}$$ about a pivot calculated?

Accepted Answer

$$	au_{net} = \sum 	au_i$$

Question 14

A force $$F is $$applied at an angle $$	heta to a $$lever arm of length $$r. $$Which of the following gives the magnitude of the torque?

Accepted Answer

$$	au = rF\sin(	heta)$$

Question 15

In a statics problem, why might you choose a particular point as the pivot?

Accepted Answer

To minimize the number of forces that produce torque about that point

Question 16

Which of the following is a correct statement about forces acting at zero distance from the pivot?

Accepted Answer

They produce zero torque.

Question 17

A weightlifter holds a barbell stationary above their head. Which type of equilibrium is demonstrated?

Accepted Answer

Both translational and rotational equilibrium

Question 18

Which of the following is true about the direction of torque?

Accepted Answer

It depends on the direction of the force and the position vector.

Question 19

If a force is applied directly towards or away from the pivot, what is the resulting torque?

Accepted Answer

Zero torque

Rotational Motion: Torque, Rigid Body Equilibrium, and Moment of Inertia

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