11.1 – Frames of Reference and Relativity

Inertial Frame of Reference (IFOR) a frame of reference in which the law of inertia holds The FOR must be at a constant velocity (not speed) or at rest In both, net force = 0N

a) Pick-up at const vel b) Earth is stationary

Non-Inertial Frame of Reference (NIFOR) a frame of reference that does not obey the law of inertia the reference involves acceleration. (A Nonzero Net Force)

From inside the accelerating car, the ball appears to move without a force acting on it (Breaks Newt’s 2 nd Law)

Guidelines for IFOR’s 1. An inertial frame of reference is one which an object has no net force acting on it; and it is at rest or moving at a constant velocity.

Guidelines for IFOR’s 2. The laws of Newtonian mechanics are only valid in an inertial frame of reference.

Guidelines for IFOR’s 3. The laws of Newtonian mechanics apply equally in all inertial frames of reference.

In an IFOR, you cannot tell if you are moving or not Your FOR could be moving at a constant vel. and you would never know

Special Theory of Relativity What would happen if you are moving at the speed of light in a car and then you turn your headlights on? This is the type of thought experiment Einstein performed to conceptualize movement at very high speeds (closer to speed of light)

Special Theory of Relativity 1.The relativity principle: - all the laws of physics are valid in all inertial frames of reference - All laws of physics includes laws governing electricity, magnetism and optics

Special Theory of Relativity 2. The consistency of the speed of light: light travels through empty space with a speed of c = 3.00 X 10 8 m/s relative to all inertial frames of reference. Einstein defined light as the universal speed limit

Simultaneity The occurrence of two or more events at the same time is a relative concept Two events that are simultaneous in one FOR are in general not simultaneous in a second FOR moving with respect to the first Simultaneity is not an absolute concept

Thought Experiment Two FOR’s: Stationary outside a train, stationary inside a train When the train, travelling at v forward, passes the outside observer a double photon gun releases two photons. One towards the front and one towards the back. What will the two observers see? Will the photons hit the front and back of the train at the same time?

Think about: Two supernovas are visible from Earth at exactly the same time

Relativity of Time, Length and Momentum

Time dilation: the effect of time occurring slower in one system compared to another system. Note: As objects move faster relative to the Earth, time slows down.

Note: Dilation means widening, thus time dilation means widening time. Proper time occurs when an observer remains in one system of time.

Thought Experiment – Time Dilation The light clock

Applications of Time Dilation Applicable to all biological, technological, physical processes

 t s =  t M /[1-(v 2 /c 2 )] 0.5 where  t S = equivalent time spent moving from perspective of stationary observer  t M = change in time for observer in stationary FOR v = speed of moving observer ( in m/s) c = speed of light ( 3.00 X 10 8 m/s)

Do photons experience time? Flight of the Navigator

GPS Satellites are in orbit travelling at approximately 14,000 km/hr. Due to special relativity, how much will the clock on the satellite have to be sped up or slowed down per day to be even with a clock on Earth?

Example # 1: A person travels for 3.0 years at the speed 0.70c relative to a physics student on Earth. Calculate the time that has passed for the student.

Solution  t m =  t s /[(1-(v 2 /c 2 )] 0.5  t m = (3.0 years)/[1- (0.70c) 2 /c 2 ] 0.5 = 4.2 years The time from the students perspective is 4.2 years.

The Twin Paradox Einstein had a thought experiment involving two twins, in which one went to a star at a speed near the speed of light and then came back to Earth.

Which twin would be older?

The one on Earth?

Or the one on the spacecraft?

Proper Length: the length of an object at rest Length Contraction: the shortening of distances in a system as seen by an observer in motion relative to that system.

Length contraction only occurs in the direction of motion

L m = L s (1- v 2 /c 2 ) 0.5 Where L m = length for moving observer L s = length for stationary observer v = speed of moving observer ( in m/s) c = speed of light ( 3.00 X 10 8 m/s)

Example # 2: Calculate the proper length of an object that has a L m = 45 m when it is moving at 0.60c.

Solution L m = L s (1- v 2 /c 2 ) 0.5 L s = L m /(1- v 2 /c 2 ) 0.5 = (45 m) /[1- (0.60c) 2 /c 2 ] 0.5 = 56 m The proper length is 56 m.

Example # 3 If two spaceships, 40m long, are travelling towards each other at 0.20c and 0.30c, what will each pilot see as the length of the other ship?

Relativistic Momentum: the momentum of an object travelling at a speed at 0.10c or greater.

p = mv/(1- v 2 /c 2 ) 0.5 where p = magnitude of relativistic momentum (in kgm/s) m = rest mass (in kg) v = speed of an object (in m/s)

Rest Mass The mass of an object as measured from a frame of reference at which the object is not moving

Relavistic Momentum Accounts for the fact that mass changes as an objects speeds up Conservation of momentum still holds

Example # 3: Calculate the magnitude of relativistic momentum of an object that has a mass of 600 kg at a speed of 0.80c.

Solution p = mv/(1- v 2 /c 2 ) 0.5 p = (600kg)(0.80)(3.00X10 8 ms) [1-(0.80c) 2 /c 2 ] 0.5 p = 2.4 X kgm/s The magnitude of relativistic momentum is 2.4 X kgm/s.

11.2 Practice Questions Page 573 Questions 1-3 Page 576 Questions 5-9 Page 578 Questions 10,11 Page 579 Questions 1- 5