Causes of Circular Motion Chapter 7, Section 2 & 3 Pg

Tangential Speed Tangential Speed (v t ) is the instantaneous linear speed of an object at any point in its circular path. vtvtvtvt vtvtvtvt vtvtvtvt

How do we calculate the tangential speed? Vt = rω Tangential Speed radius angular speed

Sample Problem The radius of a CD in a computer is 0.06 m. If a microbe riding on the disc’s rim has a tangential speed of 1.88 m/s what is the disc’s angular speed? I’m getting dizzy!!! Vt = rω Vt = 1.88 m/s r = 0.06 m ω = Vt/r ω = (1.88 m/s)/ (0.06 m) ω = 31.3 rad/s

Tangential Acceleration Tangential acceleration (a t ) is the instantaneous linear acceleration of an object at any point in its circular path. atatatat

Tangential Speed: Vt = rω How do we calculate the tangential acceleration? Acceleration measures the change in speed over a given amount of time. Vt/ Δ t =rΔω/ΔtrΔω/Δta t = Angular acceleration: α = Δ ω/ Δ t a t = rα

Sample Problem A spinning ride at a carnival has an angular acceleration of 0.50 rad/s². How far is a rider from the center of the ride if his tangential acceleration is 3.3 m/s²? a t = 3.3 m/s² α = 0.50 rad/s² a t = rα r = a t /α r = (3.3 m/s²) / (0.50 rad/s²) r = 6.6 m r = ?

Centripetal Acceleration Centripetal acceleration (a c ) is the acceleration that is directed towards the center of a circular path. atat acac

Calculating Centripital Acceleration a c = v t ²/r or Since Vt = rω a c = (rω)²/r a c = rω²

Sample Problem What is the tangential speed of a test car moving at a constant speed around a circular track that is 48.2 m from the track’s center and has a centripetal acceleration of 8.05 m/s²? a c = v t ²/r v t ² = (a c )(r) v t = √(a c )(r)= √ (8.05 m/s²) (48.2 m) v t = 19.7 m/s a c = 8.05 m/s² r = 48.2 m v t = ?

Forces that maintain circular motion acac What is causing an object to move in a circular motion? a t and v t Centripetal acceleration is only part of the answer! What causes a c to occur in the first place?

ANSWER = CENTRIPETAL FORCE!!! Any object that experiences a circular motion has a force directed towards its center axis (F c ). FcFc v t and a t a t and v t

Centripetal force can be defined as: F c = ma c Since a c = v t ²/r = rω² F c = mv t ²/r F c = mrω²

Sample Problem A pilot is flying a small plane at 30 m/s in a circular path with a radius of m. If a force of 635 N is needed to maintain the pilot’s circular motion, what is the pilot’s mass? v t = 30 m/s r = m F c = 635 N F c = mv t ²/r m = F c (r)/vt² m = (635 N)(100.0 m)/ (30 m/s)² m = 70.6 kg

Homework Assignment Practice: Pg. 255 # 2 Pg. 256 # 1 Pg. 258 # 1, 4 Pg. 261 # 1,3 Pre-AP: Pg. 270 # 18 & 20