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?

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

Question 1

A 1.0-kg solid disk of diameter 20.0 cm rotates at 200 rpm. A 1.0-kg circular loop of the same diameter is dropped onto the disk and accelerates due to friction until it rotates together with the disk. What is the final angular velocity of the combined system? (Assume no external torques.)

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

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

Question 4

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

Accepted Answer

$$\sum v = 0$$

Question 5

A person holds their head erect. The center of mass of the head is not directly above the principal point of support. Which force must the neck muscles exert to keep the head erect?

Accepted Answer

A force that creates a counterclockwise torque equal in magnitude to the gravitational torque

Question 6

Which of the following best describes neutral equilibrium?

Accepted Answer

The object remains in its new position after being disturbed

Question 7

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

Accepted Answer

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

Question 8

Which physical quantity is described by $$L = I \omega$$?

Accepted Answer

Angular momentum

Question 9

A beam is subjected to a compressive force. Which type of stress is present?

Accepted Answer

Compression

Question 10

Which of the following statements about static equilibrium is correct?

Accepted Answer

The sum of all forces and the sum of all torques on the object must be zero

Question 11

A solid disk and a circular loop, both of mass $$m$$ and radius $$R$$, rotate together after friction brings them to the same angular velocity. What is the combined moment of inertia?

Accepted Answer

$$I = \frac{1}{2} m R^2$ + m R^2$

Question 12

Which of the following is the correct expression for Young's modulus $$E$$?

Accepted Answer

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

Question 13

A system is in static equilibrium. Which of the following must be true about the net force and net torque?

Accepted Answer

Both net force and net torque are zero

Question 14

Which scenario best illustrates unstable equilibrium?

Accepted Answer

A ball balanced on top of a hill that rolls away when disturbed

Question 15

Which of the following is a real-world example of bulk stress?

Accepted Answer

Water pressure acting equally in all directions on a submerged object

Question 16

If the sum of the torques about any pivot is not zero, what will happen to the system?

Accepted Answer

The system will rotate

Question 17

Which of the following is the correct formula for the area of a circular cross-section with radius $$r$$?

Accepted Answer

$$A = \pi r^2$

Question 18

A ladder is in static equilibrium leaning against a wall. Which force prevents it from sliding?

Accepted Answer

Friction force at the base

Question 19

Which of the following is a correct application of the second law for rotation in static equilibrium?

Accepted Answer

$$\sum 	au = 0$$

Question 20

Which of the following is a correct statement about the forces acting on a body in static equilibrium?

Accepted Answer

All forces and torques are balanced

Rotation, Static Equilibrium, and Stress-Strain: Physics Concepts for General Science

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