From the case we know that:
- The moment of inertia Icm of the uniform flat disk witout the point mass is Icm = MR².
- The moment of inerta with respect to point P on the disk without the point mass is Ip = 3MR².
- The total moment of inertia (of the disk with the point mass with respect to point P) is I total = 5MR².
Please refer to the image below.
We know from the case, that:
m = 2M
r = R
m2 = 1/2M
distance between the center of mass to point P = p = R
Distance of the point mass to point P = d = 2R
We know that the moment of inertia for an uniform flat disk is 1/2mr². Then the moment of inertia for the uniform flat disk is:
Icm = 1/2mr²
Icm = 1/2(2M)(R²)
Icm = MR² ... (i)
Next, we will find the moment of inertia of the disk with respect to point P. We know that point P is positioned at the arc of the disk. Hence:
Ip = Icm + mp²
Ip = MR² + (2M)R²
Ip = 3MR² ... (ii)
Then, the total moment of inertia of the disk with the point mass is:
I total = Ip + I mass
I total = 3MR² + (1/2M)(2R)²
I total = 3MR² + 2MR²
I total = 5MR² ... (iii)
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Answer:
Explanation:
The form of Newton's 2nd Law that we use for this is:
F - f = ma where F is the Force pulling the mass down the ramp forward, f is the friction trying to keep it from moving forward, m is the mass and a is the acceleration (and our unknown).
We know mass and we can find f, but we don't have F. But we can solve for that by rewriting our main equation to reflect F:
That's everything we need.
w is weight: 6.0(9.8). Filling in:
6.0(9.8)sin20 - .15(6.0)(9.8) = 6.0a and
2.0 × 10¹ - 8.8 = 6.0a and
11 = 6.0a so
a = 1.8 m/s/s
The answer here is prism. The light passing through prism experiences bending of its multiple wavelength composition which allows it to visibly shows the difference in each of the light's color wavelength, violet bending the most while the least is the color red.
His total displacement from his original position is -1 m
We know that total displacement of an object from a position x to a position x', d = final position - initial position.
d = x' - x
If we assume the lad's initial position in front of her house is x = 0 m. The lad then moves towards the positive x-axis, 5 m. He then ends up at x' = 5 m. He then finally goes back 6 m.
Since displacement = final position - initial position, and his displacement is d' = -6 m (since he moves in the negative x - direction or moves back) from his initial position of x' = 5 m.
His final position, x" after moving back 6 m is gotten from
x" - x' = -6 m
x" = -6 + x'
x" = -6 + 5
x" = -1 m
Thus, his total displacement from his original position is
d = final position - initial position
d = x" - x
d = -1 m - 0 m
d = -1 m
So, his total displacement from his original position is -1 m
Learn more about displacement here:
brainly.com/question/17587058
Consider the upward direction of motion as positive and downward direction of motion as negative.
a = acceleration due to gravity in downward direction = - 9.8 
v₀ = initial velocity of rock in upward direction = ?
v = final velocity of rock at the highest point = 0 
t = time to reach the maximum height = 4.2 sec
Using the kinematics equation
v = v₀ + a t
inserting the values
0 = v₀ + (- 9.8) (4.2)
v₀ = 41.2
