<span>1.7 rad/s
The key thing here is conservation of angular momentum. The system as a whole will retain the same angular momentum. The initial velocity is 1.7 rad/s. As the person walks closer to the center of the spinning disk, the speed will increase. But I'm not going to bother calculating by how much. Just remember the speed will increase. And then as the person walks back out to the rim to the same distance that the person originally started, the speed will decrease. But during the entire walk, the total angular momentum remained constant. And since the initial mass distribution matches the final mass distribution, the final angular speed will match the initial angular speed.</span>
Answer:
2.69 m/s
Explanation:
Hi!
First lets find the position of the train as a function of time as seen by the passenger when he arrives to the train station. For this state, the train is at a position x0 given by:
x0 = (1/2)(0.42m/s^2)*(6.4s)^2 = 8.6016 m
So, the position as a function of time is:
xT(t)=(1/2)(0.42m/s^2)t^2 + x0 = (1/2)(0.42m/s^2)t^2 + 8.6016 m
Now, if the passanger is moving at a constant velocity of V, his position as a fucntion of time is given by:
xP(t)=V*t
In order for the passenger to catch the train
xP(t)=xT(t)
(1/2)(0.42m/s^2)t^2 + 8.6016 m = V*t
To solve this equation for t we make use of the quadratic formula, which has real solutions whenever its determinat is grater than zero:
0≤ b^2-4*a*c = V^2 - 4 * ((1/2)(0.42m/s^2)) * 8.6016 m =V^2 - 7.22534(m/s)^2
This equation give us the minimum velocity the passenger must have in order to catch the train:
V^2 - 7.22534(m/s)^2 = 0
V^2 = 7.22534(m/s)^2
V = 2.6879 m/s
Answer:
Explanation:
for baseball
(a) Let the mass of the baseball is m.
radius of baseball is r.
Total kinetic energy of the baseball, T = rotational kinetic energy + translational kinetic energy
T = 0.5 Iω² + 0.5 mv²
Where, I be the moment of inertia and ω be the angular speed.
ω = v/r
T = 0.5 x 2/3 mr² x v²/r² + 0.5 mv²
T = 0.83 mv²
According to the conservation of energy, the total kinetic energy at the bottom is equal to the total potential energy at the top.
m g h = 0.83 mv²
where, h be the height of the top of the hill.
9.8 x h = 0.83 x 6.8 x 6.8
h = 3.93 m
(b) Let the velocity of juice can is v'.
moment of inertia of the juice can = 1/2mr²
So, total kinetic energy
T = 0.5 x I x ω² + 0.5 mv²
T = 0.5 x 0.5 x m x r² x v²/r² + 0.5 mv²
m g h = 0.75 mv²
9.8 x 3.93 = 0.75 v²
v = 7.2 m/s
Answer:
The frequency is 
Explanation:
From the question we are told that
The frequency of the tuning fork is 
The beat period is 
Generally the beat frequency is mathematically represented as
The beat frequency is also represented mathematically as
Where 
is the frequency of the piano
So
Answer:
Less than 1 m
Explanation:
When objects are getting closer to each other there is a slight change in the wavelength that is being transmitted by either objects. This is known as the blue shift of waves. Here, the wavelength reduces.
In the opposite case the when objects are getting farther from each other there is a slight change in the wavelength that is being transmitted by either objects. This is known as the red shift. Here, the wavelength increases.
In this case the spaceship is getting close to Earth hence the wavelength will be lower than 1 m.
