### Short Answer

#### 8.1 Linear Momentum, Force, and Impulse

If an object’s velocity is constant, what is its momentum proportional to?

- Its shape
- Its mass
- Its length
- Its breadth

How can you express impulse in terms of mass and velocity when neither of those are constant?

- $\Delta \text{p}=\text{\Delta}(m\text{v})$
- $\frac{\text{\Delta}\text{p}}{\text{\Delta}t}=\frac{\text{\Delta}(m\text{v})}{\text{\Delta}t}$
- $\text{\Delta}\text{p}=\text{\Delta}(\frac{m}{\text{v}})$
- $\frac{\text{\Delta}\text{p}}{\text{\Delta}t}=\frac{1}{\text{\Delta}t}\text{\xb7}\text{\Delta}(m\text{v})$

How can you express impulse in terms of mass and initial and final velocities?

- $\text{\Delta}\text{p}\text{=}m\text{(}{\text{v}}_{\text{f}}-{\text{v}}_{\text{i}}\text{)}$
- $\frac{\text{\Delta}\text{p}}{\text{\Delta}t}\text{=}\frac{m\text{(}{\text{v}}_{\text{f}}-{\text{v}}_{\text{i}}\text{)}}{\text{\Delta}t}$
- $\text{\Delta}\text{p}\text{=}\frac{\text{(}{\text{v}}_{\text{f}}-{\text{v}}_{\text{i}}\text{)}}{m}$
- $\frac{\text{\Delta}\text{p}}{\text{\Delta}t}=\frac{1}{m}\frac{({\text{v}}_{\text{f}}-{\text{v}}_{\text{i}})}{\text{\Delta}t}$

Why do we use average force while solving momentum problems? How is net force related to the momentum of the object?

- Forces are usually constant over a period of time, and net force acting on the object is equal to the rate of change of the momentum.
- Forces are usually not constant over a period of time, and net force acting on the object is equal to the product of the momentum and the time interval.
- Forces are usually constant over a period of time, and net force acting on the object is equal to the product of the momentum and the time interval.
- Forces are usually not constant over a period of time, and net force acting on the object is equal to the rate of change of the momentum.

#### 8.2 Conservation of Momentum

Under what condition(s) is the angular momentum of a system conserved?

- When net torque is zero
- When net torque is not zero
- When moment of inertia is constant
- When both moment of inertia and angular momentum are constant

#### 8.3 Elastic and Inelastic Collisions

Two objects collide with each other and come to a rest. How can you use the equation of conservation of momentum to describe this situation?

*m*_{1}**v**_{1}+*m*_{2}**v**_{2}= 0*m*_{1}**v**_{1}−*m*_{2}**v**_{2}= 0*m*_{1}**v**_{1}+*m*_{2}**v**_{2}=*m*_{1}**v**_{1}′*m*_{1}**v**_{1}+*m*_{2}**v**_{2}=*m*_{1}**v**_{2}

What is the equation for conservation of momentum along the *x*-axis for 2D collisions in terms of mass and velocity, where one of the particles is initially at rest?

*m*_{1}**v**_{1}=*m*_{1}**v**_{1}′cos*θ*_{1}*m*_{1}**v**_{1}=*m*_{1}**v**_{1}′cos*θ*_{1}+*m*_{2}**v**_{2}′cos*θ*_{2}*m*_{1}**v**_{1}=*m*_{1}**v**_{1}′cos*θ*_{1}−*m*_{2}**v**_{2}′cos*θ*_{2}*m*_{1}**v**_{1}=*m*_{1}**v**_{1}′sin*θ*_{1}+*m*_{2}**v**_{2}′sin*θ*_{2}

What is the equation for conservation of momentum along the *y*-axis for 2D collisions in terms of mass and velocity, where one of the particles is initially at rest?

- 0 =
*m*_{1}**v**_{1}′sin*θ*_{1} - 0 =
*m*_{1}**v**_{1}′sin*θ*_{1}+*m*_{2}**v**_{2}′sin*θ*_{2} - 0 =
*m*_{1}**v**_{1}′sin*θ*_{1}−*m*_{2}**v**_{2}′sin*θ*_{2} - 0 =
*m*_{1}**v**_{1}′cos*θ*_{1}+*m*_{2}**v**_{2}′cos*θ*_{2}