6. two billiard balls of equal mass are traveling straight toward each other with the same speed. they meet head - on in an elastic collision. what is the total momentum of the system containing the two balls before collision? (5 pts)

7. define the following terms as used in circular motion and give their s. i units:
a) angular speed ($omega$) (2 pts)
b) angular acceleration ($alpha$) (2 pts)
c) centripetal acceleration ($a_t$) (2 pts)

8. convert the following to rad/s:
a) 900 rpm (2 pts)
b) $46^circ$/s. (2 pts)

Question

6. two billiard balls of equal mass are traveling straight toward each other with the same speed. they meet head - on in an elastic collision. what is the total momentum of the system containing the two balls before collision? (5 pts)

7. define the following terms as used in circular motion and give their s. i units:
   a) angular speed ($omega$) (2 pts)
   b) angular acceleration ($alpha$) (2 pts)
   c) centripetal acceleration ($a_t$) (2 pts)

8. convert the following to rad/s:
   a) 900 rpm (2 pts)
   b) $46^circ$/s. (2 pts)

Accepted Answer

### Question 6
# Explanation:
## Step1: Recall momentum formula
Momentum $ p = mv $, where $ m $ is mass and $ v $ is velocity.
## Step2: Define velocities of two balls
Let mass of each ball be $ m $, speed (magnitude of velocity) be $ v $. Let velocity of first ball be $ +v $ (positive direction), then velocity of second ball (moving opposite) is $ -v $.
## Step3: Calculate total momentum
Total momentum $ P = p_1 + p_2 = mv + m(-v) = mv - mv = 0 $.
# Answer:
The total momentum before collision is $ \boldsymbol{0} $ (since the two momenta are equal in magnitude and opposite in direction, they cancel out).

### Question 7
#### Part (a): Angular speed ($\omega$)
# Brief Explanations:
Angular speed is the rate of change of angular displacement ($\theta$) with time ($t$). Formula: $ \omega=\frac{\Delta\theta}{\Delta t} $. S.I. unit: radians per second (rad/s), or can also be expressed as Hz (1 Hz = 1 rad/s for angular speed in rotational context, but rad/s is standard).
# Answer:
Definition: Rate of change of angular displacement with time ($ \omega = \frac{\Delta\theta}{\Delta t} $). S.I. unit: rad/s (radians per second).

#### Part (b): Angular acceleration ($\alpha$)
# Brief Explanations:
Angular acceleration is the rate of change of angular speed ($\omega$) with time ($t$). Formula: $ \alpha=\frac{\Delta\omega}{\Delta t} $. S.I. unit: radians per second squared (rad/s²).
# Answer:
Definition: Rate of change of angular speed with time ($ \alpha = \frac{\Delta\omega}{\Delta t} $). S.I. unit: rad/s² (radians per second squared).

#### Part (c): Centripetal acceleration ($a_r$)
# Brief Explanations:
Centripetal acceleration is the acceleration of an object moving in a circular path, directed towards the center of the circle. It is due to the change in direction of velocity. Formula: $ a_r=\frac{v^2}{r}=\omega^2 r $, where $ v $ is linear speed, $ r $ is radius, $ \omega $ is angular speed. S.I. unit: meters per second squared (m/s²).
# Answer:
Definition: Acceleration of a body in circular motion directed towards the center, due to change in velocity direction. Formula: $ a_r = \frac{v^2}{r}=\omega^2 r $. S.I. unit: m/s² (meters per second squared).

### Question 8
#### Part (a): Convert 900 rpm to rad/s
# Explanation:
## Step1: Recall rpm to rad/s conversion
1 revolution = $ 2\pi $ radians, 1 minute = 60 seconds. So, to convert rpm (revolutions per minute) to rad/s: multiply by $ \frac{2\pi}{60} $ (or $ \frac{\pi}{30} $).
## Step2: Apply conversion to 900 rpm
$ 900\ \text{rpm} = 900\times\frac{2\pi}{60}\ \text{rad/s} $
Simplify: $ 900\times\frac{2\pi}{60}= 30\pi \approx 94.25\ \text{rad/s} $ (matches the handwritten calculation’s approximate value).
# Answer:
$ 900\ \text{rpm} = \boldsymbol{30\pi\ \text{rad/s} \approx 94.25\ \text{rad/s}} $

#### Part (b): Convert $ 46^\circ/\text{s} $ to rad/s
# Explanation:
## Step1: Recall degree to radian conversion
$ \pi $ radians = $ 180^\circ $, so $ 1^\circ=\frac{\pi}{180}\ \text{radians} $.
## Step2: Apply conversion to $ 46^\circ/\text{s} $
$ 46^\circ/\text{s} = 46\times\frac{\pi}{180}\ \text{rad/s} $
Calculate: $ \frac{46\pi}{180}\approx\frac{46\times3.1416}{180}\approx\frac{144.5136}{180}\approx0.803\ \text{rad/s} $ (matches the handwritten calculation’s approximate value).
# Answer:
$ 46^\circ/\text{s} = \boldsymbol{\frac{23\pi}{90}\ \text{rad/s} \approx 0.803\ \text{rad/s}} $

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QUESTION IMAGE

Question

Explanation:

Question 6

Step1: Recall momentum formula

Step2: Define velocities of two balls

Step3: Calculate total momentum

Answer:

Question 7

Part (a): Angular speed (\(\omega\))