“If a 10 kg mass travels in a circle of 5 m radius, and experiences a centripetal acceleration of 3 m/s2, what would the acceleration be if the circle were 15 m in radius, and everything else stayed the same”

“If a 1000 kg mass travels in a circle of 50 m radius, and experiences a centripetal acceleration of 5 m/s2, what would the acceleration be if the object lost half it’s mass, and everything else stayed the same”

Newton’s Law of Gravity Wanted to explain Kepler’s work Developed laws of motion en route to law of gravity 1665 speculated force that caused fall of apple kept Moon in its orbit Orbiting is falling Same laws of physics for Moon and Earth

Newton’s Law of Gravity Newton compared accelerations Acceleration  1/distance2 Accel (m/s2) Dist. (m) Ratio of acceleration Ratio of dist. Ratio2 of dist. Moon 2.52 x 10-3 4.0 x 108 1/3896 62.5 3906 apple 9.8 6.38 x 106

Newton’s Law of Gravity F  1/r2 Twice distance ¼ force 4 x distance 1/16 force ½ distance 4 x force

Newton’s Law of Gravity Galileo Big & small bodies fall with same acceleration Newton a = F/m Same a means bigger F for bigger m F  m F  m1 x m2

Newton’s Law of Gravity Put them together F  m1m2 r2 Equation F = Gm1m2 G is proportionality constant G = 6.67 x 10-11 N·m2/kg2

Gravitational Force Earth (mE = 5.98 x 1024 kg) is 1.496 x 1011 m from the the Sun (mS = 1.99 x 1030 kg) What is the gravitational force? 3.55 x 1022 N

Centripetal Force Earth (mE = 5.98 x 1024 kg) goes around the Sun in 1 year (365 days) rorbit = 1.496 x 1011 m What centripetal force is required?

Centripetal Force F = mv2/r What is the average speed of the earth? vA = xT/tT What distance does the Earth travel (m)? How long does it take to travel (s)?

Centripetal Force What is the average speed of anything? vA = xT/tT What distance does the Earth travel (m)? How long does it take to travel (s)? What is the centripetal force (N)?

Weight Newton’s Second Law W = mg What is the weight force of a 70 kg person standing on the Earth?

Weight of 70 kg person 70 kg 686 N 9.8 m/s2

Gravitational Force For spherical objects the law of gravity behaves as if all the mass is concentrated at a tiny point at the center of the sphere

Gravitational Force A person (70 kg) is standing on the surface of the Earth (mE = 5.98 x 1024 kg, rE = 6.38 x 106 m) From Newton’s Law of Gravity F = Gm1m2 r2 What is the gravitational force between the person and the Earth?

Gravitational force between person and Earth 4.38 x 109 N 3.5 x 105 N 8.23 x 10-21 N 686 N

Newton’s Law of Gravity Results Gravitational acceleration independent of mass Depends only on distance Why projectile motion is parabola F = ma  with g & r can calculate mass

Rotational Motion and Torque

Rotational Motion & Quantities In angular motion physical results depend on the distance from the axis of rotation

Rotational Motion & Quantities In a rotating CD all the parts complete a revolution in the same time Bits further from the center must move faster Bigger circumference; same time

Angular Measure Angle defined as arc length divided by radius

Radians Number of radians = arc length/radius = s/r Length around circle = 2pr Radius of circle = r 2p radians in a circle Conversion: radians to degrees 180º/p

Rotational Motion Quantities Quantities based on motion q – angular distance w – angular velocity a – angular acceleration t – time

Equations of Linear Motion x = vt a = (v – vo)/t = Dv/Dt v = vo + at va = (v + vo)/2 x = vot + ½ at2 v2 = vo2 + 2ax q = wt a = (w – wo)/t = Dw/Dt w = wo + at wa = (w + wo)/2 q = wot + ½ at2 w2 = wo2 + 2aq