Explanation:
If an object has a moment of inertia I₀ about an axis, then the moment of inertia about a different, parallel axis is I = I₀ + md², where d is the distance between the axes.
For example, consider a horizontal thin rod rotating about a vertical axis passing through its center. It has mass m and length L. Its moment of inertia is known to be I = 1/12 mL².
Now consider the same rod, but this time we move the axis of rotation L/2 to the end of the rod. We can use parallel axis theorem to find the new moment of inertia:
I = I₀ + md²
I = 1/12 mL² + m (L/2)²
I = 1/12 mL² + 1/4 mL²
I = 1/3 mL²
Positive acceleration occurs when an object speeds up.
Explanation:
Acceleration is the rate of change in velocity per unit time:
where 
is the change in velocity while 
is the time interval. From the formula, we can understand that when is positive, so when the object is speeding up, the acceleration is positive; on the contrary, when is negative (so, when the object is slowing down), the acceleration is negative.
Answer: R = 346.4N and angle 30° to the horizontal negative axis
Explanation:
To find the resultant force, we need to sum up the forces on the vertical and horizontal axis.
For the horizontal axis;
Rx = -b + acos60
Rx = -400N +200cos60
Rx = -400N +100N
Rx = -300N
For the vertical axis;
Ry = asin60 = 200sin60
Ry = 173.2N
The resultant force R can be given as;
R = √(Rx^2 +Ry^2)
R = √((-300)^2 + 173.2^2)
R = 346.4N
Angle z can be written as
Tanz = Ry/Rx
z = taninverse (Ry/Rx)
z = taninverse (173.2/300)
z = 30°
Answer: The focal length of the cornea-lens system in his eye must be LESS THAN the distance between the front and back of his eye.
Explanation:
The human eye the front part of the eye is the CORNEA. This is the tough white transparent part of the eye that helps in the refraction of light rays. While the backside of the eye is the RETINA. This is the part of the eye when images are focused.
When a normal eye is at rest, parallel rays from a distant object are focused on the retina. The ability of the eye - lens to focus points at different distances on the retina is known as accomodation. The adjustment of the eye lens to focus objects of varying distances is brought about by the ciliary muscles. The have the ability to change the shape of the eye which leads to change in focal length.
When a person with normal vision looks at a distant object at infinity, the lens brings parallel rays to focus on the retina. Thus, the furthest point which the eye can see distinctly is called the far point of the eye and it's infinity for a normal eye. But Joe was able to focus his eye on the tree, meaning that the tree was within his near point. This is the nearest point at which an object is clearly seen. Therefore, when the effective focal length of the cornea-lens system changes, it changes the location of the image of any object in one's field of view.
Answer:
Truck's speed = 5.21 m/s
Car's speed = 20.2 m/s
Explanation:
Given:
Mass of truck = M = 1650 kg
Speed of the truck initially = U = 15 m/s
Mass of the car = m = 779 kg
Initial speed of the car =u = 0
From the momentum conservation, Total initial momentum = Total final momentum.
M V+m U = M V +m v
⇒ (1650)(15) + 779×0 = (1650)V + 779 v
⇒ 24750 = 1650 V+779 v →(1)
Since the collision is elastic, relative velocity of approach = relative velocity of separation. 15 = v - V
⇒ v =V + 15; This is now substituted in the equation(1) above.
24750 = 1650 V + (799) (V+15)
⇒ 24750 = 1650 V + 799 V + 11985
⇒ 2449 V = 12765
⇒ Final velocity of the truck = 
= 5.21 m/s
Final velocity of the car = v = V+15 = 5.21 + 15 = 20.2 m/s
