Recall the formula,
∆<em>θ</em> = <em>ω</em>₀ <em>t</em> + 1/2 <em>α</em> <em>t</em> ²
where ∆<em>θ</em> = angular displacement, <em>ω</em>₀ = initial angular speed (which is zero because the disk starts at rest), <em>α</em> = angular acceleration, and <em>t</em> = time. Solve for the acceleration with the given information:
50 rad = 1/2 <em>α</em> (5 s)²
<em>α</em> = (100 rad) / (25 s²)
<em>α</em> = 4 rad/s²
Now find the angular speed <em>ω </em>after 3 s using the formula,
<em>ω</em> = <em>ω</em>₀ + <em>α</em> <em>t</em>
<em>ω</em> = (4 rad/s²) (3 s)
<em>ω</em> = 12 rad/s
The first thing that needs to be done is to find everything in the same units. 12 hours becomes 43200 seconds. Then find the distance traveled by light in that amount of time. Using the formula v=d/s, manipulate it so it looks like d=v*s. Then plug in the values: d=(3x10^8)*43200, d=1.3x10^13m. But you need to find this in kilometers. To do this, simply divide your answer by one thousand. Thus, a laser beam would travel 1.3x10^10 kilometers in 12 hours.
Hi!
We call these stars <em>main sequence </em>stars. Main sequence stars actually make up around 90% of the stars in our universe!
An interesting thing to note is that our sun is actually a <em />yellow dwarf star, which is a <em>small </em>main sequence star.
Hopefully, this helps! =)
<h3>
Answer:</h3>
Magnitude of Impulse: 30000 kg · m/s or 30000 N · s
Force on the Car: -6000 N
<h3>
General Formulas and Concepts:</h3>
<u>Math</u>
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtract Property of Equality<u>
</u>
<u>Physics</u>
<u>Momentum</u>
- Momentum Equation: P = mv
- Impulse Equation: J = FΔt
- Law of Conservation of Momentum
<h3>
Explanation:</h3>
<u>Step 1: Define</u>
Mass <em>m</em> = 1.50 × 10³ kg
Velocity <em>v</em> = 20 m/s east
Change in time Δt = 5.00 s
<u>Step 2: Find Magnitude</u>
- Substitute [Momentum]: P = (1.50 × 10³ kg)(20 m/s)
- Multiply: P = 30000 kg · m/s
<u>Step 3: Find Force</u>
<em>We use the Law of Conservation of Momentum to find our break force acting upon the car.</em>
- Substitute [Impulse]: 30000 kg · m/s = F(5.00 s)
- Rewrite: 30000 N · s = F(5.00 s)
- Divide 5 on both sides: 6000 N = F
- Rewrite: F = 6000 N
Since the car is deaccelerating, the break force would be towards the west direction (negative as east is our positive direction).
∴ F = -6000 N
Assuming the same deformation and elastic modulus, we can use the relationship:
(P/D)1 = (P/D)2
Where P is the load, Dis the diameter of the wire, 1 is the first wire, and 2 is the second wire. Using the given values and solving for the diameter of the second wire:
D = (24 / 0.24) (1)
D = 100 mm
