Q: Which condition must be satisfied for a system to be in static equilibrium?

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

Question 1

Which of the following correctly expresses the torque $$	au$$ produced by a force $$\vec{F}$$ applied at a distance $$r$$ from the axis of rotation, where $$\phi is $$the angle between $$\vec{r}$$ and $$\vec{F}$$?

Accepted Answer

$$	au = F r \sin \phi$$

Question 2

A force of 10 N is applied tangentially to the rim of a wheel of radius 0.5 m. What is the magnitude of the torque produced?

Accepted Answer

$$5\ \mathrm{N \cdot m}$$

Question 3

Which of the following statements about torque is correct?

Accepted Answer

A positive torque causes counterclockwise rotation.

Question 4

A wheel of radius $$0.350\ \mathrm{m}$$ has three forces applied as shown: $$11.9\ \mathrm{N}$$ downward, $$8.50\ \mathrm{N}$$ upward, and $$14.6\ \mathrm{N} at$$ $$40.0^\circ to $$the radius. What is the net torque about the center?

Accepted Answer

$$-0.310\ \mathrm{N \cdot m}$$

Question 5

Newton’s second law for rotation is given by which equation?

Accepted Answer

$$\sum 	au = I \alpha$$

Question 6

A cord is wrapped around the rim of a wheel of radius $$0.250\ \mathrm{m}$$, and a steady pull of $$40.0\ \mathrm{N} is $$exerted. The moment of inertia is $$5.00\ \mathrm{kg \cdot m^2$}. $$What is the angular acceleration $$\alpha$$?

Accepted Answer

$$2.0\ \mathrm{$$rad/s^2$$}$$

Question 7

Which equation correctly relates rotational work $$W to $$torque $$	au$$ and angular displacement $$\Delta 	heta$$?

Accepted Answer

$$W = 	au \Delta 	heta$$

Question 8

A 2024 Cadillac Lyriq AWD electric car produces $$610\ \mathrm{Nm} of $$torque and $$500\ \mathrm{hp} of $$power. Estimate the rotation speed of its electric motor in RPM. (1 hp = 746 W)

Accepted Answer

$$3900\ \mathrm{RPM}$$

Question 9

Which of the following is the correct expression for the angular momentum $$L of a $$rigid body?

Accepted Answer

$$L = I \omega$$

Question 10

A spinning disk of mass $$m$$ and angular speed $$6.00\ \mathrm{rad/s}$$ has a second identical disk dropped onto it. What is the final angular speed?

Accepted Answer

$$3.00\ \mathrm{rad/s}$$

Question 11

A figure skater spins with arms outstretched at $$0.40\ \mathrm{rev/s}. $$When she pulls her arms in, her moment of inertia decreases. What happens to her angular speed?

Accepted Answer

It increases.

Question 12

Which condition must be satisfied for a system to be in static equilibrium?

Accepted Answer

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

Question 13

A strut of length $$3.00\ \mathrm{m}$$ and mass $$16.0\ \mathrm{kg} is $$held by a cable at $$37.0^\circ to $$the horizontal. What is the tension in the cable?

Accepted Answer

$$104\ \mathrm{N}$$

Question 14

In the Atwood machine with $$m_1 = 2$$\ \mathrm{kg}$$, m_2$ = 4\ \mathrm{kg}$$, $$M = 3\ \mathrm{kg}$$, $$R = 0.5\ \mathrm{m}$$, what is the acceleration of either mass?

Accepted Answer

$$\frac{4}{15}g$$

Question 15

A small $$4.0\ \mathrm{kg}$$ brick is dropped from $$2.5\ \mathrm{m}$$ onto a seesaw ($$10\ \mathrm{kg}$$, $$4.0\ \mathrm{m}$$ long) and sticks. What is the angular speed just after impact?

Accepted Answer

$$1.9\ \mathrm{rad/s}$$

Question 16

Which of the following best describes the conservation of angular momentum for a rigid body?

Accepted Answer

$$I_i \omega_i = I_f \omega_f$$

Question 17

A force $$\vec{F} is $$applied at a point $$P at a $$distance $$r$$ from the axis, making an angle $$\phi$$ with $$\vec{r}. $$Which component of $$\vec{F}$$ produces torque?

Accepted Answer

$$F \sin \phi$$

Question 18

Which of the following is a correct unit for torque?

Accepted Answer

$$\mathrm{N \cdot m}$$

Question 19

If the net external torque on a system is zero, what can be said about the system’s angular momentum?

Accepted Answer

It is conserved.

Dynamics of Rotational Motion: Torque, Angular Momentum, and Statics

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