CP Physics Chapter 7 Angular Motion

180 deg =  rad 1 rot = 2  rad 1 rev = 2  rad

Example #1 What is the arc length traveled by an object moving 158 degrees if it is located 3.3 m from the center of revolution?

Example #2 Convert the following to radian: A. 30 degB. 129 deg C revD. 333 deg E. 2.5 rotF. 7 rev Convert the following to degrees: A. 1.3 radB. 3.8 rad

Angular Displacement and Velocity

Example #3 What is the angular displacement of a rotating tire with a diameter of 37 cm that spins 30 times a second? What is the total distance traveled by the rim of the tire? Angular Velocity?

Example #4 A child is riding on a merry-go-round. How far from the center is she if she travels a total distance of 55.6 m and makes 4 complete revolutions? If it took her 1 min to make 4 revs, what is her angular velocity?

Rotational Big 4

Example #5 A 37 cm diameter tire starts from rest and rotates to 10 rotations per sec in 3 sec. A.What is the angular acceleration? B. How many radians did the tire rotate through? C. How many rotations?

Example #6 A wheel rotates from rest to 15 rad/sec in 2-sec. A)What is its angular acceleration? B)How many rotations in that time?

Example #7 A dryer starts from rest and rotates 2 times until it reaches full speed of 1.5 rot/sec. A.What is the angular acceleration? B. How long will it take to do this?

Tangential Velocity and Acceleration v t = r  a t = r  Tangential Cat

Example #8 Tangential Cat is attached to a spinning fan traveling at 1.8 m/sec. If the cat is 0.8 m from the center of the fan, what is the cat’s angular speed?

Example #9 A dog on a merry-go-round undergoes 1.5 m/sec 2 which is 1.0 rad/sec 2. How far from the center is the dog?

Example #10 My father was a world known fast pitch softball pitcher who used the slingshot technique. Upon the end of his backswing, his 0.66 m arm is at rest and accelerates for 0.05 sec until he releases the ball. If the ball is thrown at 31.7 m/sec, what is the angular speed of his arm upon release of the ball, the a t, and the angular displacement?

Centripetal vs. Centrifugal Acceleration and Force Inertial vs. Noninertial reference frames Inertial vs. Noninertial reference frames F c is a net force – not an action/reaction force F c is a net force – not an action/reaction force Therefore, centrifugal force does not exist! Therefore, centrifugal force does not exist!

Centripetal Force Centripetal means “center-seeking” Centripetal means “center-seeking” It’s the force that holds an object in its circular path. It’s the force that holds an object in its circular path. The centripetal force is always directed towards the center of a rotating object. The centripetal force is always directed towards the center of a rotating object. Centripetal force is the TRUE FORCE! Centripetal force is the TRUE FORCE!

Centrifugal F o rce Centrifugal means “center-fleeing” Centrifugal means “center-fleeing” It’s the “force” that pulls you away from the center. It’s the “force” that pulls you away from the center. It’s the “force” you feel when a car takes a curve or when you’re spinning on an amusement park ride. It’s the “force” you feel when a car takes a curve or when you’re spinning on an amusement park ride. In reality, if the centripetal force were to disappear, you would fly off tangent to the circle because no force was acting on you, not because the centrifugal “force” pulled you away. In reality, if the centripetal force were to disappear, you would fly off tangent to the circle because no force was acting on you, not because the centrifugal “force” pulled you away. Centrifugal force is NOT A TRUE FORCE! Centrifugal force is NOT A TRUE FORCE!

Centripetal Acceleration/Force

Example #11 A little kid swings a yo-yo around above his head with a centripetal acceleration of 3.1 m/sec 2. If the string is 2.1 m, what is the yo- yo’s tangential speed?

Example #12 A piece of clay on a pottery wheel is about 0.2 m from the axis of rotation. If the wheel is spinning at 20.5 rad/sec, A. what is the centripetal acceleration of the clay? B. what is the tangential speed of the clay?

Example #13 A 0.9 kg mass is tied to the end of a 1.2 m string and whirled above your head 4 times every second. What is the centripetal force exerted on the mass?

Example #14 A 0.9-kg mass is tied to the end of a 1.2-m string and whirled vertically 4 times every second. A)What is the tension of the string at the top of the path? B)At the bottom of the path?

Example #15 42 m The Steel Force at Dorney Park has a radius of curvature of 42 m at the bottom of the first hill and travels at 32 m/sec. A)What do you weigh at the bottom of that hill? B)What is your force factor?

Example #16 At the top of the camelbacks riders experience a force factor of -1. If the train is moving at approximately 10 m/sec, what is the radius of curvature of the track? R = ?

Example #17 A car rounds a curve with a 50 m radius of curvature. If the coefficient of friction between the tires and road is 0.9, how fast can the car go without skidding?

Example #18 Riding the nauseating ride called the ROTOR. This ride has a radius of 2.1 m. The coefficient of friction between the wall and you is about 0.6. How fast must that cylinder rotate in order for you to stay “plastered” to the wall? Bobsled Banking

Newton’s Universal Law of Gravitation

Example #19 What is the attractive force between a 1 kg object and the Earth?

Example #20 Two guys are standing 0.5 m apart. Their masses are 80 kg and 95 kg. What is their attraction to each other?