By Max Chretien, etc.

ISBN-10: 0677134908

ISBN-13: 9780677134901

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Extra resources for Astrophysics and general relativity, - (lectures by Lynden-Bell only)

Sample text

In rotational motion, time remains the same, as changing the coordinate system does not affect the passage of time. If we substitute ∆θ for ∆x we arrive at the formula for angular velocity which is denoted by the Greek letter ω (spelled omega). 3 For the purposes of this chapter, we will always refer to ω as angular velocity. Now that we have position and speed for an object in rotational motion, the only remaining quantity we need to describe the motion of an object is acceleration. 3) Of course it is possible to also look at the three dimensional case, in which case spherical coordinates are used.

From this diagram we can see that the tension on the string, T , must equal the force on the hanging weight mw which is just mw g. We also can see that the only force acting on the cart is the tension, so by Newton’s second law we have mc a = mw g. Here mc is the mass of the cart. From this we know the acceleration of the cart. 1) We see that if we increase the mass of the cart, the acceleration will decrease. 1, then we have verified Newton’s second law. We can do this by changing the mass of the cart mc while applying the same force, and measuring the acceleration of the cart.

In the one-dimensional case for rotational motion, angular position is given by the variable θ. 1: The Cartesian and polar coordinate systems used in linear and rotational motion. 1) where ∆x is change in position and ∆t is change in time. In rotational motion, time remains the same, as changing the coordinate system does not affect the passage of time. If we substitute ∆θ for ∆x we arrive at the formula for angular velocity which is denoted by the Greek letter ω (spelled omega). 3 For the purposes of this chapter, we will always refer to ω as angular velocity.