Q: During a collision, a baseball bat exerts an average force of 800 N on a ball for 0.005 s. What is the impulse delivered to the ball?

$$J = F \Delta t = 800 \times 0.005 = 4\ \mathrm{N \cdot s}$$

Q: A rotating disk has a mass of 5.0 kg and a radius of 0.20 m. What is its moment of inertia about its center?

$$I = \frac{1}{2} m r^2$ = \frac{1}{2} \times 5.0 \times (0.20)^2$ = 0.10\ \mathrm{kg \cdot m^2$}$$

Q: Which of the following is a condition for equilibrium of an object?

$$\sum F = 0$$ and $$\sum \tau = 0$$

Q: Which vector operation is used to calculate torque as a vector?

$$\vec{\tau} = \vec{r} \times \vec{F}$$

Question 1

Which of the following best describes the law of conservation of linear momentum?

Accepted Answer

The total momentum of a system remains constant if the net external force acting on the system is zero.

Question 2

A 0.120 kg billiard ball (A) moving at 2.80 m/s strikes a stationary 0.140 kg ball (B). After the collision, ball A moves at 2.10 m/s at an angle of 35° from its original direction. What is the equation for conservation of momentum in the x-direction?

Accepted Answer

$$m_A v_{A,x} + m_B v_{B,x} = m_A v'_{A,x} + m_B v'_{B,x}$$

Question 3

Which formula correctly relates impulse to the change in momentum?

Accepted Answer

$$\vec{J} = \Delta \vec{p}$$

Question 4

During a collision, a baseball bat exerts an average force of 800 N on a ball for 0.005 s. What is the impulse delivered to the ball?

Accepted Answer

$$J = F \Delta t = 800 	imes 0.005 = 4\ \mathrm{N \cdot s}$$

Question 5

A 2.0 kg object moving at 3.0 m/s collides with a stationary 1.0 kg object. If the collision is perfectly inelastic, what is the final velocity of the combined mass?

Accepted Answer

$$v_f = \frac{m_1$ v_1$ + m_2$ v_2$}{m_1$ + m_2$} = \frac{2.0 	imes 3.0 + 1.0 	imes 0}{2.0 + 1.0} = 2.0\ \mathrm{m/s}$$

Question 6

Which of the following is true about momentum in two-dimensional collisions?

Accepted Answer

Momentum is conserved separately in both the x and y directions.

Question 7

A rotating disk has a mass of 5.0 kg and a radius of 0.20 m. What is its moment of inertia about its center?

Accepted Answer

$$I = \frac{1}{2} m r^2$ = \frac{1}{2} 	imes 5.0 	imes (0.20)^2$ = 0.10\ \mathrm{kg \cdot m^2$}$$

Question 8

The angular momentum of a rotating object is given by which formula?

Accepted Answer

$$L = I \omega$$

Question 9

A potter's wheel (uniform disk, mass 5.0 kg, diameter 0.40 m) rotates at 1.5 rev/s. A 2.8 kg clay disk (radius 0.08 m) is dropped onto the center and sticks. What is the final angular velocity of the system?

Accepted Answer

$$\omega_f = \frac{I_i \omega_i}{I_f}$$,\ where\ I_i = \frac{1}{2} m_{wheel} r_{wheel}^2,\ I_{clay} = \frac{1}{2} m_{clay} r_{clay}^2,\ I_f = I_i + I_{clay}$

Question 10

Which equation represents the rotational equivalent of Newton's second law?

Accepted Answer

$$	au = I \alpha$$

Question 11

A uniform beam of length 2.20 m and mass 10 kg is hinged at one end and held horizontally by a cable at the other end. What is the torque about the hinge due to the beam's weight?

Accepted Answer

$$	au = m g \frac{L}{2}$$

Question 12

Which of the following is a condition for equilibrium of an object?

Accepted Answer

$$\sum F = 0$$ and $$\sum 	au = 0$$

Question 13

A bolt must withstand a shear force of 3600 N with a safety factor of 7.0. If the shear strength of iron is $$\sigma = 70 	imes 10^6$\ \mathrm{N/m^2$}$$, what is the minimum diameter required?

Accepted Answer

$$d = 2 \sqrt{\frac{F_{max}}{\pi \sigma}}$$,\ where\ F_{max} = 7 	imes 3600$

Question 14

Which vector operation is used to calculate torque as a vector?

Accepted Answer

$$\vec{	au} = \vec{r} 	imes \vec{F}$$

Question 15

If the net external torque on a system is zero, what happens to the system's angular momentum?

Accepted Answer

The angular momentum remains constant.

Question 16

A wheel rotates with angular displacement $$	heta = 9.5t - 13.0t^2$ + 1.6t^3$ (radians, t$ in seconds). What is the expression for instantaneous angular velocity?

Accepted Answer

$$\omega = \frac{d	heta}{dt} = 9.5 - 26.0t + 4.8t^2$

Question 17

Which of the following statements about the center of mass (CM) is correct?

Accepted Answer

The center of mass of a system of particles lies closer to the particle with the most mass.

PHYS 215 Test #3 Review: Momentum, Impulse, and Conservation Laws

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