How much of the Moon is always illuminated one time? Explain your answer.
1 answer:
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Answer:
8.6 miles
Explanation:
We need to calculate the components of the total displacement along the east-west and north-south directions first.
In the first part, Erica moves 5.2 miles at 25∘ north of east. So the components of this displacement along the two directions are:
East:
North:
In the second part, Erica moves 5.0 miles north. So, the components of this displacement are:
East:
North:
So the components of the total displacement are
East:
North:
Therefore the magnitude of the displacement, which is the straight-line distance from the starting point to the end of the race, is
d.Both points have the same instantaneous angular velocity.
Explanation:
Let's analyze each option one by one:
a.the angular velocity at point A is greater than that of point B. --> FALSE. In fact, for a rigid body (such as the rigid wheel in this problem), all the points along the body rotates with the same angular velocity. This is because the angular velocity is defined as
where is the angular displacement and t is the time taken. Therefore, all the points rotate by the same angle
in the same time t.
b.Both points have the same centripetal acceleration. --> FALSE. The centripetal acceleration of a point along the disk is given by
where is the angular velocity and r is the distance of the point from the axis of rotation. Here A is located farther away from the axis with respect to B, so it will have a greater centripetal acceleration.
c.Both points have the same tangential acceleration. --> FALSE. The tangential acceleration is given by
where is the angular acceleration.
is the same for every point for a rigid body, but
is not (A is located farther away), so A and B do not have same tangential acceleration.
d.Both points have the same instantaneous angular velocity. --> TRUE. This is true for what we said at point A).
e.Each second, point A turns through a greater angle than point B. --> FALSE. The two points cover the same angular displacement in the same time, since they have same angular velocity.
Learn more about circular motion:
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