Q: A 3.2 kg flagpole extends from a wall at an angle of $$25^\circ$$ from the horizontal. Its center of gravity is 1.6 m from the point where the pole is attached to the wall. What is the magnitude of the gravitational torque about the point of attachment? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

$$\tau = 21.2\ \mathrm{N \cdot m}$$

Q: Which of the following is the correct form of Newton’s second law for rotational motion?

$$\tau_{\mathrm{net}} = I \alpha$$

Question 1

A wind turbine blade rotates about its central axis. If the tip of the blade is 40 m from the axis and the blade completes one revolution every 4 seconds, what is the linear speed $$v of $$the tip of the blade? (Use $$\pi = 3.14)$$

Accepted Answer

$$v = 62.8\ \mathrm{m/s}$$

Question 2

A particle moves in a circle of radius $$r$$ such that it travels an arc length $$s in $$time $$t. $$The angular position $$	heta (in $$radians) is given by which equation?

Accepted Answer

$$	heta = \dfrac{s}{r}$$

Question 3

A car tire has a radius of $$0.30\ \mathrm{m}$$ and is rolling without slipping at a speed of $$29\ \mathrm{m/s}. $$What is the angular velocity $$\omega of $$the tire?

Accepted Answer

$$\omega = 87\ \mathrm{rad/s}$$

Question 4

Which of the following statements about angular velocity $$\omega$$ and linear velocity $$v is $$correct for a point at a distance $$r$$ from the axis of rotation?

Accepted Answer

$$v = \omega r$$

Question 5

A uniform rod of length $$L$$ and mass $$M$$ rotates about one end. What is its moment of inertia $$I$$ about that end?

Accepted Answer

$$I = \dfrac{1}{3} M L^2$

Question 6

A force $$F is $$applied at a distance $$r$$ from a pivot at an angle $$\phi to $$the radial line. What is the torque $$	au$$ produced by this force?

Accepted Answer

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

Question 7

A 3.2 kg flagpole extends from a wall at an angle of $$25^\circ$$ from the horizontal. Its center of gravity is 1.6 m from the point where the pole is attached to the wall. What is the magnitude of the gravitational torque about the point of attachment? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$	au = 21.2\ \mathrm{N \cdot m}$$

Question 8

Emma (25 kg) and Noah (22 kg) are playing on a seesaw. Noah sits 1.6 m from the pivot. How far from the pivot should Emma sit to balance the seesaw? (Assume the seesaw's mass is negligible.)

Accepted Answer

$$x = 1.41\ \mathrm{m}$$

Question 9

A solid cylinder (mass $$M$$, radius $$R) $$rotates about its central axis. What is its moment of inertia $$I$$?

Accepted Answer

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

Question 10

A 540 kg flywheel (solid cylinder, radius 0.30 m) is spun up by a constant torque. If it starts from rest and reaches 13,000 rpm in 300 s, what is the angular acceleration $$\alpha$$? (1 rpm = $$2\pi/60$$ rad/s)

Accepted Answer

$$\alpha = 0.045\ \mathrm{$$rad/s^2$$}$$

Question 11

A bucket of mass $$2.5\ \mathrm{kg} is $$attached to a rope wound around a $$3.0\ \mathrm{kg}$$, $$4.0\ \mathrm{cm}$$ radius cylinder. If the bucket is released from rest $$4.0\ \mathrm{m}$$ above the ground, and the rope does not slip, which of the following best describes the acceleration of the bucket?

Accepted Answer

It is less than $$g$$ because some force accelerates the cylinder's rotation.

Question 12

A force of $$1500\ \mathrm{N} is $$applied by a rope at radius $$R to a $$capstan. A sailor pushes at a distance $$7R$$ from the axis. What force must the sailor apply to keep the capstan turning at constant speed?

Accepted Answer

$$F = 210\ \mathrm{N}$$

Question 13

Which of the following best describes the center of gravity of an object?

Accepted Answer

It is the point where the net force of gravity can be considered to act.

Question 14

A wheel is rolling without slipping. What is the velocity of the point at the bottom of the wheel relative to the ground?

Accepted Answer

It is zero.

Question 15

Which of the following is the correct form of Newton’s second law for rotational motion?

Accepted Answer

$$	au_{\mathrm{net}} = I \alpha$$

Question 16

A disk and a hoop, both with mass $$M$$ and radius $$R$$, are released from rest at the top of an incline. Which will reach the bottom first and why?

Accepted Answer

The disk, because it has a smaller moment of inertia.

Question 17

If a force is applied perpendicular to a wrench at a distance $$r$$ from the pivot, which configuration produces the maximum torque?

Accepted Answer

When the force is applied perpendicular to the wrench.

Question 18

A gymnast is suspended horizontally from a bar. Where does the gravitational torque act?

Accepted Answer

At the gymnast's center of gravity.

Question 19

Which of the following is the correct relationship between tangential acceleration $$a_t$$ and angular acceleration $$\alpha$$ for a point at radius $$r$$?

Accepted Answer

$$a_t = r \alpha$$

Rotational Motion: Physics with Calculus Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard