Answer:
The angular velocity is 15.37 rad/s
Solution:
As per the question:

Horizontal distance, x = 30.1 m
Distance of the ball from the rotation axis is its radius, R = 1.15 m
Now,
To calculate the angular velocity:
Linear velocity, v = 
v = 
v = 
v = 
Now,
The angular velocity can be calculated as:

Thus

Answer:
Approximately
for the train from Boston to NYC Penn Station.
Approximately
for the train from NYC Penn Station to Boston.
Explanation:
Convert minutes to hours:
.
.
Calculate average speed of each train:
.

Assume that it takes a time period of
for the trains to pass by each other after departure. Distance each train travelled would be:
.
.
Since the trains have just passed by each other, the sum of the two distances should be equal to the distance between the stations:
.
Rearrange and solve for
:
.
.
Distance each train travelled in
:
.
.
Answer: Energy cannot be <u>created</u> or <u>destroyed</u> just <u>changes</u> in form.
Explanation:
This is the principle of the first Law of Thermodynamics, which relates the work and the transferred energy exchanged in a system through the internal energy, which is neither created nor destroyed, it is only transformed.
In other words: The total energy of a system is always conserved.
Answer:
Explanation:
a ) When the box starts to slip
static friction = mg sinα
mg cosα x μ = mg sinα ( μ is coefficient of static friction )
Tanα = μ = .35
α = 19.2°
b ) Once box starts moving , kinetic friction will start applying on it
kinetic friction = mg cos19.2 x .25
= 2.31m
net force downward = mgsin19.2 - mgcos19.2 x .25
= m ( 3.22 - 2.31 )
= .91 m
acceleration downward ( a ) = .91 m / s²
c )
v² = u² + 2 a s
= 0 + 2 x .91 x 5
= 9.1
v = 3 m / s
The masses of both objects and the distance between their centers.