Q: A 20-kg ladder leans against a frictionless wall at an angle of $$\theta = 60^\circ. $$The coefficient of friction between the ladder and the floor is $$\mu. $$What is the minimum value of $$\mu$$ required to prevent the ladder from sliding?

$$\mu = \dfrac{1}{2 \tan \theta}$$

Q: A ladder of length $$l$$ and mass $$m$$ leans against a frictionless wall at angle $$\theta. $$Which equation correctly relates the torque due to gravity about the base to the normal force at the wall?

$$m g \dfrac{l}{2} \sin \theta = F_{N2} l \cos \theta$$

Question 1

A 20.0-cm diameter, 1.0-kg solid disk is rotating at 200 rpm. A 20.0-cm diameter, 1.0-kg circular loop is dropped straight down onto the disk and accelerates due to friction until it is 'riding' the disk. What is the final angular velocity of the combined system? (Assume no external torques and both objects rotate together after contact.)

Accepted Answer

$$\omega_f = 7.0\ \mathrm{rad/s}$$

Question 2

Which equation correctly expresses the conservation of angular momentum for the disk and loop system described above?

Accepted Answer

$$I_1$$ \$$omega_1$$ = ($$I_1$$ + $$I_2$$) \$$omega_2$$

Question 3

A 20-kg ladder leans against a frictionless wall at an angle of $$	heta = 60^\circ. $$The coefficient of friction between the ladder and the floor is $$\mu. $$What is the minimum value of $$\mu$$ required to prevent the ladder from sliding?

Accepted Answer

$$\mu = \dfrac{1}{2 	an 	heta}$$

Question 4

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

Accepted Answer

$$\sum F_x = m a_x$$

Question 5

A person holds their head erect, but the center of mass of the head is not directly above the principal point of support. If the mass of the head is $$m$$ and the distance from the pivot to the center of mass is $$r_g$$, what is the torque due to gravity?

Accepted Answer

$$	au_g = m g r_g$$

Question 6

A 0.5-mm diameter, 60-mm long graphite pencil lead (Young's modulus $$E = 1 	imes 10^9$\ \mathrm{N/m^2$}) is $$subjected to a 4 N force. What is the change in length $$\Delta l$$?

Accepted Answer

$$\Delta l = \dfrac{F l_0$}{E \pi r^2$}$$

Question 7

Which type of equilibrium is characterized by an object returning to its original position after a small perturbation?

Accepted Answer

Stable equilibrium

Question 8

In the context of stress and strain, which formula defines Young's modulus $$E$$?

Accepted Answer

$$E = \dfrac{F/A}{\Delta l / l_0$}$$

Question 9

A solid disk and a circular loop of equal mass and radius are rotating together after friction brings them to the same angular velocity. Which statement about their combined moment of inertia is correct?

Accepted Answer

$$I_{total} = \dfrac{1}{2} M R^2$ + M R^2$

Question 10

Which of the following best describes the role of free-body diagrams (FBDs) in solving static equilibrium problems?

Accepted Answer

They help identify all forces and torques acting on the system.

Question 11

A ladder of length $$l$$ and mass $$m$$ leans against a frictionless wall at angle $$	heta. $$Which equation correctly relates the torque due to gravity about the base to the normal force at the wall?

Accepted Answer

$$m g \dfrac{l}{2} \sin 	heta = F_{N2} l \cos 	heta$$

Question 12

Which of the following is a correct statement about neutral equilibrium?

Accepted Answer

After a small displacement, the object stays in its new position.

Question 13

If a system is in static equilibrium, which of the following must be true for the sum of torques about any pivot?

Accepted Answer

$$\sum 	au = 0$$

Question 14

Which of the following best describes bulk stress?

Accepted Answer

Stress applied uniformly in all directions within a material.

Question 15

A force $$F is $$applied to a rod of length $$l_0$$ and cross-sectional area $$A. If $$the rod's Young's modulus is $$E$$, what is the strain experienced by the rod?

Accepted Answer

$$	ext{Strain} = \dfrac{\Delta l}{l_0$}$$

Question 16

Which of the following is true about the torque produced by a force $$F$$ applied at a distance $$r$$ from a pivot?

Accepted Answer

$$	au = F r$$

Question 17

A system is said to be in static equilibrium if:

Accepted Answer

It is at rest and the net force and net torque on it are zero.

Question 18

Which of the following is the correct expression for the moment of inertia of a solid disk of mass $$M$$ and radius $$R$$?

Accepted Answer

$$I = \dfrac{1}{2} M R^2$

Question 19

Which of the following statements about stress and strain is correct?

Accepted Answer

Stress is the force per unit area, and strain is the fractional change in length.

Rotation, Static Equilibrium, and Stress-Strain: PHYS 120 Lecture 19 Study Notes

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