Q: Two forces, $$F_1 = 100$$ \text{ N}$$ and F_2$ = 200 \text{ N}$$, act on a 2-m bar at angles of $$30^\circ$$ with the bar, both at a distance of 0.7 m from one end. What is the net torque about the axis at the end?

$$\tau_{net} = 0.7 \times (100 \sin 30^\circ + 200 \sin 30^\circ) = 105 \text{ Nm}$$

Q: A seesaw of length $$L$$ and mass $$M is $$balanced at its midpoint. Two kids of masses $$m_1$$ and $$m_2$$ sit at the ends. What is the net torque about the midpoint immediately after they sit down?

$$\tau_{net} = \frac{L}{2} (m_1$ g - m_2$ g)$$

Q: A man holds a 6-kg barbell with his arm extended horizontally, arm length 0.54 m, and arm mass 4 kg. What is the net torque about his shoulder due to the barbell and his arm's weight?

$$\tau_{net} = (6 \times 9.8 \times 0.54) + (4 \times 9.8 \times 0.27)$$

Q: A composite disc is acted on by three forces, each of 10 N, at different radii and angles. How do you calculate the net torque about the center?

Sum the individual torques: $$\tau_{net} = \sum r_i F_i \sin \theta_i$$, using the correct sign for each.

Q: A square with sides of 4 m is free to rotate about an axis perpendicular to its face and through its center. Four forces of 100 N act simultaneously at the corners, each at an angle of $$30^\circ. $$What is the net torque about the axis?

$$\tau_{net} = 4 \times 2 \times 100 \sin 30^\circ = 400 \text{ Nm}$$

Q: A fishing pole of length 3 m and mass 2 kg is held horizontally. A fish pulls with a force of 40 N at $$20^\circ$$ below the axis at the end of the pole. What is the torque about the axis of rotation at your hands?

$$\tau = 3 \times 40 \sin 20^\circ$$

Q: A 4-m long rod of mass 20 kg is pivoted at one end and held at $$37^\circ$$ above the horizontal. What is the torque due to its weight about the pivot?

$$\tau = 20 \times 9.8 \times 2 \sin 37^\circ$$

Question 1

Which of the following best describes the relationship between force and torque in rotational dynamics?

Accepted Answer

Force causes linear acceleration, while torque causes rotational acceleration.

Question 2

A solid disc of mass $$M$$ and radius $$R is $$free to rotate about a fixed axis. A force $$F is $$applied tangentially at its edge. What is the angular acceleration $$\alpha of $$the disc?

Accepted Answer

$$\alpha = \frac{F R}{\frac{1}{2} M R^2$}$$

Question 3

Suppose you apply a force $$F at a $$distance $$r$$ from the axis of rotation, at an angle $$	heta to $$the lever arm. What is the magnitude of the torque $$	au$$ produced?

Accepted Answer

$$	au = r F \sin 	heta$$

Question 4

A wrench is 0.25 m long. You need to produce a torque of 100 Nm to tighten a bolt. What is the minimum force required if you apply the force perpendicular to the wrench?

Accepted Answer

$$F = 400 	ext{ N}$$

Question 5

Two forces, $$F_1 = 100$$ 	ext{ N}$$ and F_2$ = 200 	ext{ N}$$, act on a 2-m bar at angles of $$30^\circ$$ with the bar, both at a distance of 0.7 m from one end. What is the net torque about the axis at the end?

Accepted Answer

$$	au_{net} = 0.7 	imes (100 \sin 30^\circ + 200 \sin 30^\circ) = 105 	ext{ Nm}$$

Question 6

A seesaw of length $$L$$ and mass $$M is $$balanced at its midpoint. Two kids of masses $$m_1$$ and $$m_2$$ sit at the ends. What is the net torque about the midpoint immediately after they sit down?

Accepted Answer

$$	au_{net} = \frac{L}{2} (m_1$ g - m_2$ g)$$

Question 7

Which equation correctly relates torque $$	au$$, moment of inertia $$I$$, and angular acceleration $$\alpha$$?

Accepted Answer

$$	au = I \alpha$$

Question 8

A man holds a 6-kg barbell with his arm extended horizontally, arm length 0.54 m, and arm mass 4 kg. What is the net torque about his shoulder due to the barbell and his arm's weight?

Accepted Answer

$$	au_{net} = (6 	imes 9.8 	imes 0.54) + (4 	imes 9.8 	imes 0.27)$$

Question 9

Which of the following statements about the sign of torque is correct?

Accepted Answer

Torque is positive if it causes counterclockwise rotation and negative if it causes clockwise rotation.

Question 10

A composite disc is acted on by three forces, each of 10 N, at different radii and angles. How do you calculate the net torque about the center?

Accepted Answer

Sum the individual torques: $$	au_{net} = \sum r_i F_i \sin 	heta_i$$, using the correct sign for each.

Question 11

A square with sides of 4 m is free to rotate about an axis perpendicular to its face and through its center. Four forces of 100 N act simultaneously at the corners, each at an angle of $$30^\circ. $$What is the net torque about the axis?

Accepted Answer

$$	au_{net} = 4 	imes 2 	imes 100 \sin 30^\circ = 400 	ext{ Nm}$$

Question 12

Which of the following is the correct expression for the moment of inertia $$I of a $$solid disc of mass $$M$$ and radius $$R$$ about its center?

Accepted Answer

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

Question 13

A fishing pole of length 3 m and mass 2 kg is held horizontally. A fish pulls with a force of 40 N at $$20^\circ$$ below the axis at the end of the pole. What is the torque about the axis of rotation at your hands?

Accepted Answer

$$	au = 3 	imes 40 \sin 20^\circ$$

Question 14

Which principle can be used to solve both linear and rotational motion problems, especially when energy is conserved?

Accepted Answer

Conservation of Energy

Question 15

A 4-m long rod of mass 20 kg is pivoted at one end and held at $$37^\circ$$ above the horizontal. What is the torque due to its weight about the pivot?

Accepted Answer

$$	au = 20 	imes 9.8 	imes 2 \sin 37^\circ$$

Question 16

Which of the following is true about the axis of rotation and the direction of torque?

Accepted Answer

Torque is maximized when the force is perpendicular to the lever arm.

Question 17

A system consists of two masses $$m_1$$ and $$m_2$$ connected by a string over a pulley (solid cylinder, mass $$M$$, radius $$R). $$What is the torque on the pulley when the masses are released?

Accepted Answer

$$	au = R (m_1$ g - m_2$ g)$$

Question 18

Which of the following is the correct formula for the torque produced by a force $$F at a $$distance $$r$$ from the axis, at an angle $$	heta$$?

Accepted Answer

$$	au = r F \sin 	heta$$

Torque & Rotational Dynamics: Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards