3.4 Linear and Angular Speed

Linear Speed

Suppose a point P moves at a constant speed along a circle of radius r and center O. The measure of how fast the position of P is changing is called linear speed, v.

Angular Speed The measure of how fast the angle changes as P moves along the circle is called angular speed, ω

Linear Speed

Example

Suppose that P is on a circle with radius 15 in., and ray OP is rotating with angular speed radian per sec.

a) Find the angle generated by P in 10 sec.

b) Find the distance traveled by P along the circle in 10 sec.

c) Find the linear speed of P in inches per second.

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Example

A belt runs a pulley of radius 5 in. at 120 revolutions per min.

a) Find the angular speed of the pulley in radians per second.

b) Find the linear speed of the belt in inches per second.

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Example

A satellite traveling in a circular orbit approximately 1800 km. above the surface of Earth takes 2.5 hrs. to make an orbit. The radius of the earth is approximately 6400 km.

a) Approximate the linear speed of the satellite in kilometers per hour.

b) Approximate the distance the satellite travels in 3.5 hrs.

Ans: