Linear & Angular Speed Applications of radians, Sec. 3.4.

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Presentation transcript:

Linear & Angular Speed Applications of radians, Sec. 3.4

Linear Speed (v) Where s is the arc length traced by point P at time t

Angular Speed (ω) Measure of how fast an angle is changing θ in radians ω in radians per unit of time Relates linear and angular speed.

Example 1 Using Linear & Angular Speed Formulas

Example 2 Finding angular speed of a pulley & linear speed of a belt A belt runs a pulley of radius 5 in at 120 rpm. a.) Find the angular speed of the pulley in radians per second.

Example 2 Finding angular speed of a pulley & linear speed of a belt A belt runs a pulley of radius 5 in at 120 rpm. b.) Find the linear speed of the belt in inches per second.

Example 3 Finding linear speed & distance traveled by a satellite A satellite traveling in a circular orbit approximately 1800 km above the surface of the Earth takes 2.5 hr to make an orbit. a.) Approximate the linear speed of the satellite in km/hr.

Example 3 Finding linear speed & distance traveled by a satellite A satellite traveling in a circular orbit approximately 1800 km above the surface of the Earth takes 2.5 hr to make an orbit. b.) Approximate the distance the satellite travels in 3.5 hr.