Q: Which of the following correctly expresses the relationship between net torque and angular acceleration for a rigid body?

$$\sum \vec{\tau} = I \vec{\alpha}$$

Q: A wheel of radius $$0.350\ \mathrm{m}$$ has a force of $$11.9\ \mathrm{N}$$ applied perpendicular to its rim. What is the magnitude of the torque produced?

$$\tau = 4.17\ \mathrm{N \cdot m}$$

Question 1

Which of the following correctly expresses the relationship between net torque and angular acceleration for a rigid body?

Accepted Answer

$$\sum \vec{	au} = I \vec{\alpha}$$

Question 2

A force $$F is $$applied at a distance $$r$$ from the axis of rotation, making an angle $$\phi$$ with the position vector $$\vec{r}. $$What is the torque produced by this force?

Accepted Answer

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

Question 3

Which statement best describes the sign convention for torque?

Accepted Answer

Positive torque causes counterclockwise rotation; negative torque causes clockwise rotation.

Question 4

A wheel of radius $$0.350\ \mathrm{m}$$ has a force of $$11.9\ \mathrm{N}$$ applied perpendicular to its rim. What is the magnitude of the torque produced?

Accepted Answer

$$	au = 4.17\ \mathrm{N \cdot m}$$

Question 5

Which of the following is the correct formula for the moment arm $$l$$ when a force is applied at an angle $$\phi to $$the position vector $$\vec{r}$$?

Accepted Answer

$$l = r \sin \phi$$

Question 6

A figure skater pulls in his arms during a spin, reducing his moment of inertia. What happens to his angular velocity, assuming no external torque acts?

Accepted Answer

His angular velocity increases.

Question 7

A disk of moment of inertia $$I_1$$ spins at angular velocity $$\$$omega_1$$. A second disk of moment of inertia I_2$ (initially at rest) is dropped onto it and they stick together. What is the final angular velocity $$\omega_f$$?

Accepted Answer

$$\omega_f = \dfrac{I_1$ \$$omega_1$$}{I_1$ + I_2$}$$

Question 8

Which physical quantity is conserved in the absence of a net external torque?

Accepted Answer

Angular momentum

Question 9

A force $$F is $$applied at a point on a lever arm at a distance $$r$$ from the pivot. If the force is not perpendicular to the lever, which component of the force produces torque?

Accepted Answer

The component perpendicular to the lever arm

Question 10

A seesaw of mass $$6.0\ \mathrm{kg}$$ and length $$4.0\ \mathrm{m} is $$pivoted at its center. A $$2.0\ \mathrm{kg}$$ brick is dropped onto one end and sticks. What principle allows you to calculate the angular speed after the collision?

Accepted Answer

Conservation of angular momentum

Question 11

A cable holds a uniform beam of length $$3.00\ \mathrm{m}$$ and mass $$6.0\ \mathrm{kg} at an $$angle of $$37.0^\circ$$ with the horizontal. What is the tension $$T in $$the cable?

Accepted Answer

$$T = \dfrac{mg}{\sin 37.0^\circ}$$

Question 12

Which equation correctly relates rotational work to torque and angular displacement?

Accepted Answer

$$W = 	au \Delta 	heta$$

Question 13

A car's engine produces a torque $$	au$$ and rotates at angular speed $$\omega. $$What is the power output?

Accepted Answer

$$P = 	au \omega$$

Question 14

If the net force and net torque on a system are both zero, what can be said about the motion of the system?

Accepted Answer

The system will move with constant velocity and constant angular velocity.

Question 15

A cord is wrapped around the rim of a wheel of radius $$0.250\ \mathrm{m}$$ and moment of inertia $$I = 0.5\ \mathrm{kg \cdot m^2$}. A$$ $$2.0\ \mathrm{kg}$$ mass hangs from the cord. What is the angular acceleration $$\alpha of $$the wheel? (Neglect friction.)

Accepted Answer

$$\alpha = \dfrac{m g r}{I}$$

Question 16

Which of the following best describes the role of the patella in the human knee, in terms of torque?

Accepted Answer

It increases the moment arm of the quadriceps force, increasing the torque produced about the knee.

Question 17

A rotating rigid body has angular momentum $$L = I \omega. If $$the moment of inertia $$I is $$doubled and no external torque acts, what happens to $$\omega$$?

Accepted Answer

$$\omega is $$halved.

Question 18

Which of the following is NOT a correct way to calculate torque?

Accepted Answer

$$	au = F r \cos \phi$$

Question 19

A force $$F$$ acts at a distance $$r$$ from the axis of rotation, but along the line of action passing through the axis. What is the torque produced?

Accepted Answer

Zero

Dynamics of Rotational Motion: Study Notes

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