PHYS 1003 Lecture Notes - Lecture 5: Circular Motion, Angular Frequency, Radian

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lemonwasp446

12 Oct 2016

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Velocity vector always perpendicular to displacement vector. The circular motion is uniform when speed of rotation is constant. Velocity will vary with time because the direction is always changing (due to inward acceleration) The velocity is always tangential to the circular path. The acceleration vector always points towards the centre of the circle (centripetal acceleration) The centripetal acceleration has a magnitude given by: The period of rotation, t, is the time taken to complete one complete circle: T = circumference of a circle/linear speed. The number of revolutions per unit time is the frequency, f: When we measure angles, the radian is the unit that must be used. 1 circle = 1 revolution = 360* = 2 radians. The variable w is the angular frequency. But the radian is a dimensionless measure, so s-1 is okay. Angular frequency is related to frequency and period by.

Related Questions

Introduction

This experiment involves centripetal force, the force that keeps objects moving in a circular path. This force is perpendicular to the motion and directed towards the centre of the circular orbit. By Newton's Second law when a centripetal force acts on a mass (in the horizontal plane), the force continually changes the direction of the velocity accounts for the centripetal acceleration of the mass, whose direction is towards the centre. The relationship between the centripetal force, the mass of the orbiting object, and its speed and distance from the centre are described by:

Extension Question:

When twirling the mass, students found that despite their best efforts, they could not swing the ball so that the cord remained exactly horizontal.

On the diagram of the rotating mass below, draw a force diagram of the force acting on the mass and identify each force. Don't include any force component in this diagram.

aquamarinehound670

A particle P moves with constant angular speed ω around a circle whose center is at the origin and whose radius is R. The particle is said to be in uniform circular motion. Assume that the motion is counterclockwise and that the particle is at the point (R,0) when t=0. The position vector at time t≥0 is r(t)=Rcosωt i + Rsinωt j.

(a) Find the velocity vector v and show that v⋅r=0. Conclude that v is tangent to the circle and points in the direction of the motion.

(b) Show that the speed |v| of the particle is the constant ωR. The period T of the particle is the time required for one complete revolution. Conclude that

T=2πR/|v|=2π/ω

rosebeaver397

A particle P moves with constant angular speed ω around a circle whose center is at the origin and whose radius is R.The particle is said to be in a uniform circular motion. Assume that the motion is counterclockwise and that the particle is at the point (R, 0) when t = 0.The position vector at time t ≥ 0 is r(t) = R cos ωt i + R sin ωt j.

(a) Find the velocity vector v and show that v · r = 0. Conclude that v is tangential to the circle and points in the direction of the motion.

(b) Show that the speed of the particle is constant ωR. The period T of the particle is the time required for one complete revolution. Conclude T = 2π/ω.

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PHYS 1003 Lecture Notes - Lecture 5: Circular Motion, Angular Frequency, Radian

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