When does a simple pendulum execute simple harmonic motion? When it is oscillating at a small angle. is the relationship between the period and the length of a simple pendulum? The period squared is proportional to the length. Calculate the spring constant = 7.39 k = = (7.39)2(0.06) = 3.28 N m-1 Calculate the length of the spring when the mass is at rest. F = -k (extension) mg = -k (extension) {we can ignore the minus sign it exists merely to signify that the restoring – force and the extension are opposite in direction} (0.06)(9.8) = 3.28(extension) Extension = 0.18 m Length of string = 0.5 + 0.18 = 0.68 m 2018 Question 6 (a) Derive an expression to show the relationship between the radius, velocity and angular velocity of an object moving in uniform circular motion.  {divided both sides by t} but = and = v ω =  v = ω rω Calculate the angular velocity of the discus immediately prior to its release. = 17 rads s-1 the centripetal force acting on the discus just before Ashton releases it. F = = (2)(1.2)(17)2 = 693.6 N mrω2 In what direction does this force apply? Towards the centre 2017 Question 6 State the principle of conservation of energy. Energy cannot be created or destroyed but only converted from one form to another Derive the expression for uniform accelerated motion. v2=u2+2as {multiply out both sides} (v)2 (u v2 = u2 + v = u + at = + at)2 2uat + (at)2 v2 = u2 + 2a(ut + ½ at2) {because v2 = u2 + 2as s =ut + ½ at2}
When does a simple pendulum execute simple harmonic motion? When it is oscillating at a small angle. is the relationship between the period and the length of a simple pendulum? The period squared is proportional to the length. Calculate the spring constant = 7.39 k = = (7.39)2(0.06) = 3.28 N m-1 Calculate the length of the spring when the mass is at rest. F = -k (extension) mg = -k (extension) {we can ignore the minus sign – it exists merely to signify that the restoring force and the extension are opposite in direction} (0.06)(9.8) = 3.28(extension) Extension = 0.18 m Length of string = 0.5 + 0.18 = 0.68 m 2018 Question 6 (a) Derive an expression to show the relationship between the radius, velocity and angular velocity of an object moving in uniform circular motion. {divided both sides by t} but = ω and = v ω =  v = rω Calculate the angular velocity of the discus immediately prior to its release. = 17 rads s-1 the centripetal force acting on the discus just before Ashton releases it. F = mrω2 = (2)(1.2)(17)2 = 693.6 N In what direction does this force apply? Towards the centre 2017 Question 6 State the principle of conservation of energy. Energy cannot be created or destroyed but only converted from one form to another Derive the expression v2=u2+2as for uniform accelerated motion. v = u + at {multiply out both sides} (v)2 = (u + at)2 v2 = u2 + 2uat + (at)2 v2 = u2 + 2a(ut + ½ at2) v2 = u2 + 2as {because s =ut + ½ at2} 
4.%20Circular%20Motion%20and%20SHM.docx