# Help with Length contraction of ruler at 60degree angle to observer

• dcarmichael
In summary, length contraction is a phenomenon in which a moving object appears shorter when observed by a stationary observer. When the object is viewed at a 60 degree angle, its length will appear even shorter due to its motion relative to the observer. The amount of length contraction can be calculated using a specific formula, and it increases as the angle of motion increases. In physics, length contraction is important to consider when making calculations and measurements in fields such as astrophysics and particle physics. Real-world examples of length contraction at a 60 degree angle include the motion of a spacecraft in orbit and a person's body on a roller coaster.
dcarmichael
Homework Statement
7. A meter stick is moving with speed 0.8c relative to a frame S .
(a) What is the stick’s length, as measured by observers in S , if the stick is parallel
to its velocity v ?
(b) What if the stick is perpendicular to v ?
(c) What if the stick is at  60 to v , as seen in the stick’s rest frame? [Hint: You can
imagine that the meter stick is the hypotenuse of a 30-60-90 right triangle]
(d) What if the stick is at  60 to v , as measured in S ?
I believe i have solved a-c , but cant figure out d, looking suggestions?
Relevant Equations
L=Lo*sqrt (1-β^2)
told to use this equation and not lorentz transformation for this problem

dcarmichael said:
(d) What if the stick is at  60 to v , as measured in S ?
...cant figure out d, looking suggestions?
There are different ways to solve this. One approach is to first find the value of ##\theta '## (the angle that the stick makes to the x'-axis in the primed frame). A hint for doing that is to consider how ##\tan \theta'## is related to ##\tan 60^o##.

## 1. What is length contraction?

Length contraction is a phenomenon in which an object moving at high speeds appears shorter in the direction of its motion when observed by an outside observer.

## 2. How does length contraction occur at a 60 degree angle?

When an object is moving at high speeds at a 60 degree angle to an observer, the observer perceives the object as shorter in the direction of its motion due to the effects of special relativity.

## 3. What is the formula for calculating length contraction?

The formula for calculating length contraction is L = L0 * √(1 - v2/c2), where L0 is the rest length of the object, v is its velocity, and c is the speed of light.

## 4. Does length contraction affect all objects in motion?

Yes, length contraction affects all objects in motion, regardless of their size or mass. However, the effects are only noticeable at very high speeds close to the speed of light.

## 5. How does length contraction relate to time dilation?

Length contraction and time dilation are two sides of the same coin in the theory of special relativity. Time dilation refers to the slowing down of time for a moving object, while length contraction refers to the shortening of length for a moving object. Both effects occur due to the relative motion between the object and the observer.

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