9/13/2023 0 Comments Circular motion equations![]() ![]() ![]() A particle executing circular motion can be described by its position vector r (t). Thus, the angular velocity is approximately 8. Equations of Motion for Uniform Circular Motion. Thus, the linear velocity is approximately 70.34 centimeters per second. If the radius of the circle shown in Figure 3 is 8 centimeters, find the linear and angular velocities of point P. The angular velocity (ω) of a point traveling at a constant speed along an arc of a circle is given as:Īngular and linear velocity are both positive if the movement is counterclockwise and negative if the movement is clockwise.Įxample 4: Point P revolves counterclockwise around a point 0 making 7 complete revolutions in 5 seconds. Thus, the linear velocity of the object is 1,060 miles per hour. The linear velocity (v) of a point traveling at a constant speed along an arc of a circle is given as:Įxample 3: If the earth has a radius of 4,050 miles and rotates one complete revolution (2π radians) each 24 hours, what is the linear velocity of an object located on the equator? ![]() Thus, the length of the intercepted arc is −12.25 centimeters. (In this problem, the negative value of the angle and the arc length refer to a negative direction.) Thus, the length of the intercepted arc is 15 centimeters.Įxample 2: Using Figure 2 , find the length (s) of the arc intercepted by a central angle of size − 100° if the radius of the circle is 7 centimeters. Remember, α must be measured in radians.Įxample 1: Find the length (s) of the arc intercepted by a central angle of size 3 radians if the radius of the circle is 5 centimeters (see Figure 1). If α is the measure of a central angle of a circle, measured in radians, then the length of the intercepted arc (s) can be found by multiplying the radius of the circle (r) by the size of the central angle (α) s = rα. Graphs: Special Trigonometric Functions. ![]()
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