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

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

Question 1

In an Atwood machine, two masses $$m_1$$ and $$m_2$$ are connected by a string over a pulley. If $$m_2$$ \u003e $$m_1$$, what is the acceleration $$a of $$the system? (Assume the pulley and string are massless and frictionless.)

$$ a = \frac{m_2$ - m_1$}{m_1$ + m_2$} g $$

Accepted Answer

$$ a = \frac{m_2$ - m_1$}{m_1$ + m_2$} g $$

Question 2

A force $$F is $$applied at a distance $$r$$ from the pivot at an angle $$	heta to $$the lever arm. What is the formula for the torque $$	au$$ produced by this force?

Accepted Answer

$$ 	au = rF\sin	heta $$

Question 3

Which of the following is the correct SI unit for torque?

Accepted Answer

N m

Question 4

A seesaw is balanced with a 30 kg child sitting 2 m from the pivot on one side. Where should a 20 kg child sit on the other side to balance the seesaw?

Accepted Answer

3 m from the pivot

Question 5

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 6

A door is pushed with a force $$F at $$different points and directions as shown. In which case is the torque zero?

Accepted Answer

When $$F is $$applied at the hinge

Question 7

A rod is acted upon by four forces: $$F_1 = 2$$\,\mathrm{N}$$ at 1$$\,\mathrm{m}$$, F_2$ = 4\,\mathrm{N} at$$ $$1\,\mathrm{m}$$, $$F_3 = 2$$\,\mathrm{N}$$ at 1$$\,\mathrm{m}$$, and F_4$ = 4\,\mathrm{N} at$$ $$1\,\mathrm{m}$$, with $$F_4 at$$ $$30^\circ to $$the rod. What is the net torque about the pivot?

Accepted Answer

$$ 0 $$

Question 8

A person holds a 5 kg weight steady in their hand with their forearm horizontal. If the biceps attaches 4 cm from the elbow and the weight is 30 cm from the elbow, what is the force in the biceps? (Assume $$g = 9.8\,\mathrm{m/s^2$}$$ and ignore the weight of the forearm.)

Accepted Answer

$$ F_{biceps} = 389\,\mathrm{N} $$

Question 9

Which of the following best describes the moment of inertia?

Accepted Answer

A measure of an object's resistance to changes in its rotational motion

Question 10

A force of $$20\,\mathrm{N} is $$applied at an angle of $$60^\circ to a $$lever arm $$2\,\mathrm{m}$$ from the pivot. What is the magnitude of the torque produced?

Accepted Answer

$$ 17.3\,\mathrm{Nm} $$

Question 11

In the context of rotational motion, which equation is analogous to Newton's Second Law $$\vec{F} = m\vec{a}$$?

Accepted Answer

$$ \sum 	au = I\alpha $$

Question 12

A stationary rigid body is acted upon by several forces. Which of the following statements is true if the object is in static equilibrium?

Accepted Answer

Both the net force and net torque are zero.

Question 13

A force is applied at an angle to a wrench to loosen a bolt. Which component of the force is responsible for producing torque?

Accepted Answer

The component perpendicular to the wrench

Question 14

If $$m_2$$ \gg $$m_1 in an $$Atwood machine, what is the acceleration of the system?

Accepted Answer

$$ a = g $$

Question 15

A rod is pivoted at one end and a force $$F is $$applied at the other end perpendicular to the rod. If the length of the rod is $$L$$, what is the torque about the pivot?

Accepted Answer

$$ 	au = FL $$

Question 16

Which of the following best describes the direction of torque produced by a force applied to a rotating object?

Accepted Answer

It is perpendicular to both the position vector and the force

Question 17

A force of $$10\,\mathrm{N} is $$applied tangentially to a wheel of radius $$0.5\,\mathrm{m}. $$What is the torque produced?

Accepted Answer

$$ 5\,\mathrm{Nm} $$

Question 18

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

Accepted Answer

$$ \sum \vec{a} = 0 $$

Torque, Rotational Dynamics, and Static Equilibrium

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