Q: A planet with a diameter of 300 m completes one orbit around the sun in 250 years. What is the angular velocity $$\omega of $$the planet in radians per second?

$$\omega = \dfrac{2\pi}{250 \times 365 \times 24 \times 3600}$$

Q: A force of 20 N is applied perpendicular to a wrench at a distance of 0.5 m from the pivot. What is the torque produced?

$$\tau = 0.5 \times 20 = 10 Nm$$

Q: The impulse $$J$$ delivered to an object is equal to the change in its momentum. Which equation expresses this relationship?

$$J = F_{\text{avg}} \Delta t = \Delta p$$

Question 1

A planet with a diameter of 300 m completes one orbit around the sun in 250 years. What is the angular velocity $$\omega of $$the planet in radians per second?

Accepted Answer

$$\omega = \dfrac{2\pi}{250 	imes 365 	imes 24 	imes 3600}$$

Question 2

Which of the following correctly relates the linear speed $$v of an $$object moving in a circle of radius $$r to $$its angular speed $$\omega$$?

Accepted Answer

$$v = r \omega$$

Question 3

If an object rotates $$2\pi$$ radians every 20 seconds, what is its angular speed $$\omega$$?

Accepted Answer

$$\omega = \dfrac{2\pi}{20}$$

Question 4

A child is riding a merry-go-round with a radius of 5 m at an angular speed of $$0.3$$ rad/s. What is the child's linear speed?

Accepted Answer

$$v = 0.3 	imes 5 = 1.5 m/s$$

Question 5

Which equation correctly expresses the relationship between torque $$	au$$, force $$F$$, and the lever arm $$r$$?

Accepted Answer

$$	au = r F \sin(	heta)$$

Question 6

A force of 20 N is applied perpendicular to a wrench at a distance of 0.5 m from the pivot. What is the torque produced?

Accepted Answer

$$	au = 0.5 	imes 20 = 10 Nm$$

Question 7

Which of the following best describes the moment of inertia $$I$$ for a point mass $$m at a $$distance $$r$$ from the axis of rotation?

Accepted Answer

$$I = m r^2$

Question 8

Newton's Second Law for Rotation states that the net torque $$	au$$ produces angular acceleration $$\alpha$$ according to which equation?

Accepted Answer

$$	au = I \alpha$$

Question 9

A uniform rod of length $$L$$ and mass $$M is $$pivoted at one end. What is its moment of inertia about the pivot?

Accepted Answer

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

Question 10

A spring with spring constant $$k is $$stretched by a distance $$\Delta L. $$According to Hooke's Law, what is the force exerted by the spring?

Accepted Answer

$$F = -k \Delta L$$

Question 11

A cable with Young's modulus $$Y$$ and cross-sectional area $$A$$ supports a mass $$m$$ over a length $$L. $$What is the extension $$\Delta L of $$the cable?

Accepted Answer

$$\Delta L = \dfrac{m g L}{A Y}$$

Question 12

Which of the following statements about momentum conservation in a collision is correct?

Accepted Answer

Total momentum is conserved if no external forces act on the system.

Question 13

The impulse $$J$$ delivered to an object is equal to the change in its momentum. Which equation expresses this relationship?

Accepted Answer

$$J = F_{	ext{avg}} \Delta t = \Delta p$$

Question 14

A ball of mass $$m$$ moving at velocity $$v$$ collides with a stationary ball of equal mass in a perfectly elastic collision. What is the velocity of the first ball after the collision?

Accepted Answer

It comes to rest, $$v' = 0$$

Question 15

Which of the following best describes the center of gravity of a solid object?

Accepted Answer

It is the point where the object's total gravitational force can be considered to act.

Question 16

A system is in equilibrium if which of the following conditions are satisfied?

Accepted Answer

Net force and net torque on the system are both zero.

Question 17

A rotating disk has a constant angular acceleration $$\alpha. $$Which equation gives the angular velocity $$\omega$$ after time $$t if $$the initial angular velocity is $$\$$omega_0$$?

Accepted Answer

$$\omega = \$$omega_0$$ + \alpha t$$

Question 18

Which of the following correctly expresses the tangential acceleration $$a_t of a $$point on a rotating object?

Accepted Answer

$$a_t = r \alpha$$

Question 19

A force is applied at an angle $$	heta to a $$lever arm $$r. $$Which value of $$	heta$$ produces the maximum torque?

Accepted Answer

$$	heta = 90^\circ$$

Rotational Motion, Equilibrium, Elasticity, and Momentum: Structured Study Notes

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