Answer:
(i) 0.121 kg m²
(ii) 0.363 kg m²/s
(iii) 2 rad/s
Explanation:
(i) The moment of inertia of a rod about its end is:
I = 1/3 mr²
where m is the mass and r is the length.
Given m = 1.2 kg and r = 0.55 m:
I = 1/3 (1.2 kg) (0.55 m)²
I = 0.121 kg m²
(ii) Angular momentum is the moment of inertia times the angular velocity:
L = Iω
L = (0.121 kg m²) (3 rad/s)
L = 0.363 kg m²/s
(iii) This time, the moment of inertia of the putty is included.
I = 1/3 mr² + Mr²
I = 0.121 kg m² + (0.2 kg) (0.55 m)²
I = 0.1815 kg m²
Angular momentum is conserved:
L = Iω
0.363 kg m² = (0.1815 kg m²) ω
ω = 2 rad/s
Burning a log because you are turning the log into ash from wood.
Answer:
1.69 * 10^(-7) C
Explanation:
We can find this by using the formula for electric potential while making charge the subject of formula:
V = kQ/r
=> Q = (V*r)/k
Where k = Coulumbs constant
V = electric potential
Q = charge
r = distance between doorknob and charged body
From the question,
V = 6 kV = 6000 V
r = (25 + 0.3) cm = 25.3 cm = 253m
Note: Since we assume that the body is a sphere and we know that the charge in a sphere is concentrated in it's center, we add the radius of the sphere to the length of the spark (which tells us the distance between the doorknob and body) to get the distance between the doorknob and the charge.
Hence:
Q = (6000 * 0.253)/(9 * 10^9)
Q = 1.69 * 10^(-7) C
Answer:
The first two statements are false
The third statement is true
Explanation:
<u>The dot product assures that the integrand is always nonnegative.</u>
The dot product may be negative, this could ocurr when the vectors are directed oposite each other, for example take the unitary vector i and -i its doct product will give -1.
Another way to consider this is to take the definition of the dot product in terms of teh angle between the vetcors:
When θ>π :
cos(θ)<0
<u>The dot product indicates that only the component of the force perpendicular to the path contributes to the integral</u>
In fact the dot product is a projection of the vectors, the perpendicular component may be obtained using the cross product
<u>The dot product indicates that only the component of the force parallel to the path contributes to the integral.</u>
This one is true, since the dot product gives the projection of one vector to another, that is, the parallel component of the vector among the other one
Answer:
60 km/hour.
Explanation:
We'll begin by calculating the total distance traveled by the car. This is illustrated below:
Total distance traveled = sum of distance between PQRST
Total distance = 10 + 5 + 10 + 5
Total distance = 30 km
Next, we shall convert 30 mins to hour. This can obtained as follow:
Recall:
60 mins = 1 hour
Therefore,
30 mins = 30/60 = 0.5 hour.
Finally, we shall determine the average speed of the car as follow:
Distance = 30 km
Time = 0.5 hour
Speed =?
Speed = distance /time
Speed = 30/0.5
Speed = 60 km/hour
Therefore, the speed of the car is 60 km/hour.