(a) What angle in radians is subtended by an arc 1.50 m long on the circumference of a circle of radius 2.50 m? What is this angle in degrees? (b) An arc 14.0 cm long on the circumference of a circle subtends an angle of 128o. What is the radius of the circle? (c) The angle between two radii of a circle with radius 1.50 m is 0.700 rad. What length of arc is intercepted on the circumference of the circle by the two radii?
Solution 1E Step 1: Data given Arc length s = 1.50 m Radius r = 2.50 m The angle is given by using s = r Thus we have = s/r Substituting values we get = 1.50 m/2.50 m = 0.6 × (180/) 0 = 34.37 0 Hence we have angle as 34.37 Step 2 : Data given Arc length s = 14.0 cm Radius r = Angle = 128 = 2.23 rad The angle is given by using s = r Thus we have r = s/ Substituting values we get r = 14.0 cm /2.23 r = 6.27 cm Hence we have the radius as 6.27 cm