Question 1

A 20.0 cm wrench is used to generate a torque at a bolt.A force of 50 N is applied at the end of the wrench at an angle of 60.0 degrees to the wrench.The torque generated at the bolt is

Accepted Answer

E

Question 2

A 30.0 cm wrench is used to generate a torque at a bolt.A force of 50.0 N is applied at the end of the wrench at an angle of 70.0 degrees.The torque generated at the bolt is

Accepted Answer

B

Question 3

A 6.00 kg mass is located at (2.00 m,2.00 m,2.00 m)and a 5.00 kg mass is located at (-1.0 m,3.00 m,-2.00 m).If this system of masses rotated about the Y-axis perpendicular to the Z-X plane,then the moment of inertia of this system is

Accepted Answer

The moment of inertia of a system of masses about an axis is the sum of the moments of inertia of the individual masses about that axis. The moment of inertia of a point mass m about an axis a distance r from the mass is mr^2. In this case, the moment of inertia of the 6.00 kg mass about the Y-axis is (6.00 kg)(2.00 m)^2 = 24.00 kg m^2. The moment of inertia of the 5.00 kg mass about the Y-axis is (5.00 kg)(3.00 m)^2 = 45.00 kg m^2. Therefore, the moment of inertia of the system of masses about the Y-axis is 24.00 kg m^2 + 45.00 kg m^2 = 69.00 kg m^2.

Question 4

A 5.00 kg mass is located at (2.00 m,0.00 m,3.00 m)and a 2.00 kg mass is located at (0.00 m,4.00 m,-2.00 m).The center of gravity of the system of masses is

Accepted Answer

The center of gravity (CG) of a system of masses can be found using the formula $\text{CG} = \frac{\sum m_i \vec{r}_i}{\sum m_i}$, where $m_i$ are the masses and $\vec{r}_i$ are the position vectors of the masses. For the given system, the CG in the x, y, and z directions can be calculated as follows:- For the x-direction: $\text{CG}_x = \frac{(5 \times 2) + (2 \times 0)}{5 + 2} = \frac{10}{7}$ m.- For the y-direction: $\text{CG}_y = \frac{(5 \times 0) + (2 \times 4)}{5 + 2} = \frac{8}{7}$ m.- For the z-direction: $\text{CG}_z = \frac{(5 \times 3) + (2 \times -2)}{5 + 2} = \frac{11}{7}$ m.Therefore, the center of gravity of the system is at $(10/7 m, 8/7 m, 11/7 m)$.

Question 5

The moment of inertia of a rod being rotated about one end is 1/3 ML².What is the moment of inertia of a rod of length L and mass M being rotated about a point located 0.300 L?

Accepted Answer

The moment of inertia of a rod about an axis through one end is 1/3 ML^2. The moment of inertia about an axis through the center of mass is 1/12 ML^2. The moment of inertia about an axis parallel to the axis through the center of mass and a distance d from it is 1/12 ML^2 + Md^2. So, the moment of inertia of a rod of length L and mass M being rotated about a point located 0.300 L from one end is 1/12 ML^2 + M(0.300 L)^2 = 0.123 ML^2.

Question 6

A 20.0 cm wrench is used to generate a torque at a bolt.A force of 50 N is applied perpendicularly at the end of the wrench.The torque generated at the bolt is

Accepted Answer

Torque is calculated as the product of force and the perpendicular distance from the pivot point. Here, torque = 50 N * 0.20 m = 10 N.m.

Question 7

The moment of inertia of a rod being rotated about one end is 1/3 ML².What is the moment of inertia of a rod of length L and mass M being rotated about a point located 0.40 L?

Accepted Answer

The answer of The moment of inertia of a rod...

Question 8

A 6.00 kg mass is located at (2.00 m,2.00 m,2.00 m)and a 5.00 kg mass is located at (-1.0 m,3.00 m,-2.00 m).If this system of masses rotated about the X-axis perpendicular to the Z-Y plane,then the moment of inertia of this system is

Accepted Answer

The moment of inertia about the X-axis is calculated using I = Σm*r^2, where r is the perpendicular distance from the axis. For the 6.00 kg mass, r = sqrt((2.00)^2 + (2.00)^2) = sqrt(8) m. For the 5.00 kg mass, r = sqrt((3.00)^2 + (-2.00)^2) = sqrt(13) m. Thus, I = 6*(sqrt(8))^2 + 5*(sqrt(13))^2 = 113 kg m^2.

Question 9

A 5.00 kg mass is located at (2.00 m,0.00 m,0.00 m)and a 3.00 kg mass is located at (0.00 m,4.00 m,0.00 m).The center of gravity of the system of masses is

Accepted Answer

The center of gravity (CG) can be found using the formula $\text{CG} = \frac{\sum m_i \vec{r}_i}{\sum m_i}$, where $m_i$ are the masses and $\vec{r}_i$ are the position vectors of the masses. For the x-coordinate of the CG, $\text{CG}_x = \frac{(5.00 \, \text{kg} \cdot 2.00 \, \text{m}) + (3.00 \, \text{kg} \cdot 0.00 \, \text{m})}{5.00 \, \text{kg} + 3.00 \, \text{kg}} = \frac{10.00}{8.00} = 1.25 \, \text{m}$. For the y-coordinate, $\text{CG}_y = \frac{(5.00 \, \text{kg} \cdot 0.00 \, \text{m}) + (3.00 \, \text{kg} \cdot 4.00 \, \text{m})}{5.00 \, \text{kg} + 3.00 \, \text{kg}} = \frac{12.00}{8.00} = 1.50 \, \text{m}$. Therefore, the center of gravity is at (1.25 m, 1.50 m, 0).

Question 10

A torque of 15.0 N.m is applied to a bolt.The bolt rotates through an angle of 360 degrees.The work done in turning the bolt is

Accepted Answer

Work done by torque is calculated using the formula: Work = Torque × Angular Displacement. The angular displacement should be in radians, so 360 degrees is 2π radians. Therefore, Work = 15.0 N.m × 2π = 94.2 J.

Question 11

A centrifuge has a rotational inertia of 5.50 $\times$ 10^-3 kg m².How much energy must be supplied to bring it from rest to 500 rad/s?

Accepted Answer

The formula for rotational kinetic energy is:

$K = \frac{1}{2} I \omega^2$

where $I$ is the rotational inertia and $\omega$ is the angular velocity.

Plugging in the given values, we get:

$K = \frac{1}{2} (5.50 	imes 10^{10}	ext{ kg m}^2) (500	ext{ rad/s})^2 = 6.88 	imes 10^8	ext{ J}$.

However, the question asks how much energy must be supplied to bring the centrifuge from rest to 500 rad/s. This means that we need to find the difference between the initial and final kinetic energies, so we need to subtract the initial kinetic energy (which is zero) from the final kinetic energy:

$\Delta K = K_{final} - K_{initial} = K$

So the answer is:

$\Delta K = 6.88 	imes 10^8	ext{ J} - 0	ext{ J} = 6.88 	imes 10^8	ext{ J} \approx \boxed{	extbf{(C) } 688	ext{ J}}$.

Question 12

A 2.00 kg mass is located at (4.00 m,0.00 m,0.00 m)and a 4.00 kg mass is located at (0.00 m,3.00 m,0.00 m).If this system of masses rotated about the X-axis perpendicular to the Z-Y plane,then the moment of inertia of this system is

Accepted Answer

The answer of A 2.00 kg mass is located at...

Question 13

A 4.00 kg mass is located at (2.00 m,2.00 m,0.00 m)and a 3.00 kg mass is located at (-1 m,3.00 m,0.00 m).If this system of masses rotated about the Y-axis perpendicular to the X-Z plane,then the moment of inertia of this system is

Accepted Answer

The answer of A 4.00 kg mass is located at...

Question 14

A torque of 20.0 N.m is applied to a bolt.The bolt rotates through an angle of 180 degrees.The work done in turning the bolt is

Accepted Answer

The work done in turning the bolt can be calculated using the formula:
W = τθ
where τ is the torque applied and θ is the angle rotated.
Plugging in the given values:
W = (20.0 Nm)(180°)
W = (20.0 Nm)(π radians/180°)    (converting degrees to radians)
W = 62.8 J
Therefore, the answer is (C) 62.8 J.

Question 15

What is the rotational inertia of a solid iron disk of mass 41.0 kg with a thickness of 5.00 cm and radius of 30.0 cm,about an axis through the center and perpendicular to it?

Accepted Answer

The answer of What is the rotational inertia of a...

Question 16

A 2.00 kg mass is located at (4.00 m,0.00 m,0.00 m)and a 4.00 kg mass is located at (0.00 m,3.00 m,0.00 m).If this system of masses rotated about the Z-axis perpendicular to the X-Y plane,then the moment of inertia of this system is

Accepted Answer

The answer of A 2.00 kg mass is located at...

Question 17

A 4.00 kg mass is located at (2.00 m,2.00 m,0.00 m)and a 3.00 kg mass is located at (-1.0 m,3.00 m,0.00 m).If this system of masses rotated about the X-axis perpendicular to the Z-Y plane,then the moment of inertia of this system is

Accepted Answer

The moment of inertia about the X-axis is calculated using I = Σm*r², where r is the perpendicular distance from the axis. For the 4.00 kg mass, r = 2.00 m, so its contribution is 4*(2)² = 16 kg m². For the 3.00 kg mass, r = 1.00 m, so its contribution is 3*(1)² = 3 kg m². The total moment of inertia is 16 + 3 = 19 kg m². However, the correct calculation should consider the distance from the X-axis, which involves both y and z coordinates. The correct calculation is 4*(2² + 2²) + 3*(1² + 3²) = 32 + 11 = 43 kg m².

Question 18

A 2.00 kg mass is located at (4.00 m,0.00 m,0.00 m)and a 4.00 kg mass is located at (0.00 m,3.00 m,0.00 m).The center of gravity of the system of masses is

Accepted Answer

The answer of A 2.00 kg mass is located at...

Question 19

A 30.0 cm wrench is used to generate a torque at a bolt.A force of 40 N is applied perpendicularly at the end of the wrench.The torque generated at the bolt is

Accepted Answer

To calculate torque, we use the formula T = rF, where T is torque, r is the distance from the point of rotation to where the force is applied, and F is the force applied. In this case, r = 30.0 cm = 0.3 m and F = 40 N. Therefore, T = 0.3 m x 40 N = 12 NF1F1F1S1F1F1F10m. So the correct choice is D.

Question 20

A 6.00 kg mass is located at (2.00 m,2.00 m,2.00 m)and a 5.00 kg mass is located at (-1.0 m,3.00 m,-2.00 m).If this system of masses rotated about the Z-axis perpendicular to the X-Y plane,then the moment of inertia of this system is

Accepted Answer

The answer of A 6.00 kg mass is located at...

Quiz 8: Torque and Angular Momentum

A 20.0 cm wrench is used to generate a torque at a bolt.A force of 50 N is applied at the end of the wrench at an angle of 60.0 degrees to the wrench.The torque generated at the bolt is

A 30.0 cm wrench is used to generate a torque at a bolt.A force of 50.0 N is applied at the end of the wrench at an angle of 70.0 degrees.The torque generated at the bolt is

A 6.00 kg mass is located at (2.00 m,2.00 m,2.00 m) and a 5.00 kg mass is located at (-1.0 m,3.00 m,-2.00 m) .If this system of masses rotated about the Y-axis perpendicular to the Z-X plane,then the moment of inertia of this system is

A 5.00 kg mass is located at (2.00 m,0.00 m,3.00 m) and a 2.00 kg mass is located at (0.00 m,4.00 m,-2.00 m) .The center of gravity of the system of masses is

The moment of inertia of a rod being rotated about one end is 1/3 ML².What is the moment of inertia of a rod of length L and mass M being rotated about a point located 0.300 L?

A 20.0 cm wrench is used to generate a torque at a bolt.A force of 50 N is applied perpendicularly at the end of the wrench.The torque generated at the bolt is

The moment of inertia of a rod being rotated about one end is 1/3 ML².What is the moment of inertia of a rod of length L and mass M being rotated about a point located 0.40 L?

A 6.00 kg mass is located at (2.00 m,2.00 m,2.00 m) and a 5.00 kg mass is located at (-1.0 m,3.00 m,-2.00 m) .If this system of masses rotated about the X-axis perpendicular to the Z-Y plane,then the moment of inertia of this system is

A 5.00 kg mass is located at (2.00 m,0.00 m,0.00 m) and a 3.00 kg mass is located at (0.00 m,4.00 m,0.00 m) .The center of gravity of the system of masses is

A torque of 15.0 N.m is applied to a bolt.The bolt rotates through an angle of 360 degrees.The work done in turning the bolt is

A centrifuge has a rotational inertia of 5.50 $\times$ 10^-3 kg m².How much energy must be supplied to bring it from rest to 500 rad/s?

A 2.00 kg mass is located at (4.00 m,0.00 m,0.00 m) and a 4.00 kg mass is located at (0.00 m,3.00 m,0.00 m) .If this system of masses rotated about the X-axis perpendicular to the Z-Y plane,then the moment of inertia of this system is

A 4.00 kg mass is located at (2.00 m,2.00 m,0.00 m) and a 3.00 kg mass is located at (-1 m,3.00 m,0.00 m) .If this system of masses rotated about the Y-axis perpendicular to the X-Z plane,then the moment of inertia of this system is

A torque of 20.0 N.m is applied to a bolt.The bolt rotates through an angle of 180 degrees.The work done in turning the bolt is

What is the rotational inertia of a solid iron disk of mass 41.0 kg with a thickness of 5.00 cm and radius of 30.0 cm,about an axis through the center and perpendicular to it?

A 2.00 kg mass is located at (4.00 m,0.00 m,0.00 m) and a 4.00 kg mass is located at (0.00 m,3.00 m,0.00 m) .If this system of masses rotated about the Z-axis perpendicular to the X-Y plane,then the moment of inertia of this system is

A 4.00 kg mass is located at (2.00 m,2.00 m,0.00 m) and a 3.00 kg mass is located at (-1.0 m,3.00 m,0.00 m) .If this system of masses rotated about the X-axis perpendicular to the Z-Y plane,then the moment of inertia of this system is

A 2.00 kg mass is located at (4.00 m,0.00 m,0.00 m) and a 4.00 kg mass is located at (0.00 m,3.00 m,0.00 m) .The center of gravity of the system of masses is

A 30.0 cm wrench is used to generate a torque at a bolt.A force of 40 N is applied perpendicularly at the end of the wrench.The torque generated at the bolt is

A 6.00 kg mass is located at (2.00 m,2.00 m,2.00 m) and a 5.00 kg mass is located at (-1.0 m,3.00 m,-2.00 m) .If this system of masses rotated about the Z-axis perpendicular to the X-Y plane,then the moment of inertia of this system is

Quiz 8: Torque and Angular Momentum

A 20.0 cm wrench is used to generate a torque at a bolt.A force of 50 N is applied at the end of the wrench at an angle of 60.0 degrees to the wrench.The torque generated at the bolt is

A 30.0 cm wrench is used to generate a torque at a bolt.A force of 50.0 N is applied at the end of the wrench at an angle of 70.0 degrees.The torque generated at the bolt is

A 6.00 kg mass is located at (2.00 m,2.00 m,2.00 m) and a 5.00 kg mass is located at (-1.0 m,3.00 m,-2.00 m) .If this system of masses rotated about the Y-axis perpendicular to the Z-X plane,then the moment of inertia of this system is

A 5.00 kg mass is located at (2.00 m,0.00 m,3.00 m) and a 2.00 kg mass is located at (0.00 m,4.00 m,-2.00 m) .The center of gravity of the system of masses is

The moment of inertia of a rod being rotated about one end is 1/3 ML2.What is the moment of inertia of a rod of length L and mass M being rotated about a point located 0.300 L?

A 20.0 cm wrench is used to generate a torque at a bolt.A force of 50 N is applied perpendicularly at the end of the wrench.The torque generated at the bolt is

The moment of inertia of a rod being rotated about one end is 1/3 ML2.What is the moment of inertia of a rod of length L and mass M being rotated about a point located 0.40 L?

A 6.00 kg mass is located at (2.00 m,2.00 m,2.00 m) and a 5.00 kg mass is located at (-1.0 m,3.00 m,-2.00 m) .If this system of masses rotated about the X-axis perpendicular to the Z-Y plane,then the moment of inertia of this system is

A 5.00 kg mass is located at (2.00 m,0.00 m,0.00 m) and a 3.00 kg mass is located at (0.00 m,4.00 m,0.00 m) .The center of gravity of the system of masses is

A torque of 15.0 N.m is applied to a bolt.The bolt rotates through an angle of 360 degrees.The work done in turning the bolt is

A centrifuge has a rotational inertia of 5.50 ×\times× 10-3 kg m2.How much energy must be supplied to bring it from rest to 500 rad/s?

A 2.00 kg mass is located at (4.00 m,0.00 m,0.00 m) and a 4.00 kg mass is located at (0.00 m,3.00 m,0.00 m) .If this system of masses rotated about the X-axis perpendicular to the Z-Y plane,then the moment of inertia of this system is

A 4.00 kg mass is located at (2.00 m,2.00 m,0.00 m) and a 3.00 kg mass is located at (-1 m,3.00 m,0.00 m) .If this system of masses rotated about the Y-axis perpendicular to the X-Z plane,then the moment of inertia of this system is

A torque of 20.0 N.m is applied to a bolt.The bolt rotates through an angle of 180 degrees.The work done in turning the bolt is

What is the rotational inertia of a solid iron disk of mass 41.0 kg with a thickness of 5.00 cm and radius of 30.0 cm,about an axis through the center and perpendicular to it?

A 2.00 kg mass is located at (4.00 m,0.00 m,0.00 m) and a 4.00 kg mass is located at (0.00 m,3.00 m,0.00 m) .If this system of masses rotated about the Z-axis perpendicular to the X-Y plane,then the moment of inertia of this system is

A 4.00 kg mass is located at (2.00 m,2.00 m,0.00 m) and a 3.00 kg mass is located at (-1.0 m,3.00 m,0.00 m) .If this system of masses rotated about the X-axis perpendicular to the Z-Y plane,then the moment of inertia of this system is

A 2.00 kg mass is located at (4.00 m,0.00 m,0.00 m) and a 4.00 kg mass is located at (0.00 m,3.00 m,0.00 m) .The center of gravity of the system of masses is

A 30.0 cm wrench is used to generate a torque at a bolt.A force of 40 N is applied perpendicularly at the end of the wrench.The torque generated at the bolt is

A 6.00 kg mass is located at (2.00 m,2.00 m,2.00 m) and a 5.00 kg mass is located at (-1.0 m,3.00 m,-2.00 m) .If this system of masses rotated about the Z-axis perpendicular to the X-Y plane,then the moment of inertia of this system is

The moment of inertia of a rod being rotated about one end is 1/3 ML².What is the moment of inertia of a rod of length L and mass M being rotated about a point located 0.300 L?

The moment of inertia of a rod being rotated about one end is 1/3 ML².What is the moment of inertia of a rod of length L and mass M being rotated about a point located 0.40 L?

A centrifuge has a rotational inertia of 5.50 $\times$ 10^-3 kg m².How much energy must be supplied to bring it from rest to 500 rad/s?