Objects moving in a circle Linear speed V

Objects moving in a circle Linear speed = V Which moves faster on a merry-go-round a horse near the outside rail or a horse near the inside rail? the distance moved per unit of time S=Vt Angular speed = ω the angle moved per unit of time φ=ωt Period = T the time required for one revolution Frequency = f the number of revolutions per unit time φ

Objects moving in a circle Which moves faster on a merry-go-round a horse near the outside rail or a horse near the inside rail? r 2 The larger r – the larger V The larger ω – the larger V ω r 1

Objects moving in a circle φ=ωt one radian is the angle subtended by an arc length equal to R S=Vt S=R Time = φ/ω Time = S/V Time = 1 rad/ω Time = R/V 1 rad/ω 1/ω = R/V V = ωR R ω 1 radian

Objects moving in a circle Which moves faster on a merry-go-round a horse near the outside rail or a horse near the inside rail? r 2 The larger r – the larger V The larger ω – the larger V V = ωR Check the units! Check the limiting cases! ω r 1

Angular speed = ω the angle moved per unit of time V = ωR Period = T the time required for one revolution Frequency = f the number of revolutions per unit time R T=? f=? ω

Circular Motion: Forces F What are the objects that interact with the ball? Draw a free-body diagram for the ball at any point of its path. F F

Circular Motion: Forces When an object moves in a circle, is its velocity changing? Vf Assume that the speed of the bowling ball remains constant and find the direction of the acceleration of the ball assuming that the direction of the acceleration is the same as the direction of the velocity change vector. Vi φ

Circular Motion: Forces Vf Vi φ

Circular Motion: Forces When an object moves in a circle, is its velocity changing? Assume that the speed of the bowling ball remains almost constant and find the direction of the acceleration of the ball assuming that the direction of the acceleration is the same as the direction of the velocity change vector. Vf φ Vi

Circular Motion: Forces When an object moves in a circle, is its velocity changing? Assume that the speed of the bowling ball remains almost constant and find the direction of the acceleration of the ball assuming that the direction of the acceleration is the same as the direction of the velocity change vector. Vi Vf Two similar isosceles triangles R

Circular Motion: Forces V R

Homework (due Friday) Chapter 4. Problems # 46, 52, 54, 57 Read Sections 7. 1, 7. 3, 7. 4 Problems # 1, 9, 15

Quiz A 1000 -kg elevator on the top floor of a building starts at rest and 2. 0 sec later is moving downward at speed 4. 0 m/s. Find the magnitude of the tension in the cable pulling the elevator as speed is increasing.