Objects A and B are in uniform circular motion and both have a tangential velocity of 11.5 m/s.
a. If the period of object A is 2.4 s and the period of object B is 1.2 s, what is the ratio of the radius off object A's motion to the radius of object B's motion?
b. if the radius of object A's motion is 3.0 m and the radius of object B's motion is 1.0 m, what is the ratio of object A's acceleration to object object B's acceleration?
a. If the period of object A is 2.4 s and the period of object B is 1.2 s, what is the ratio of the radius off object A's motion to the radius of object B's motion?
b. if the radius of object A's motion is 3.0 m and the radius of object B's motion is 1.0 m, what is the ratio of object A's acceleration to object object B's acceleration?
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The period for circular motion defined as the time it takes for 1 revolution T a = 2.4 and Tb = 1.2 seconds/cycle
The Frequency for circulaar motion is the inverse of the Period or Cycles/sec Fa =1/Ta =0.417 and Fb = 1/1.2 =0.833
The Velocity of a point on the cicumference of an object with circular motion is V= WR where W (Omega) is the angular velocity in Radians /sec and R is the radi;us.
The relationshio between the frequency and the angular velocity is F= W/2pi or W= 2pi F
Wa = 2 pi Fa =2.62 Rad/sec and Wb = 2 pi Fb = 5.24 Rad/sec
Va = Vb
Wa Ra = Wb Rb
Ra/Rb = Wb/Wa = 5.24/2.62 = 2
b ) If Ra/Rb = 3/1 what is the acceleration ratio Aa/Ab ?
The acceleration that applies here ils called Normal Acceleration An and equal to W^2R and is directed toward the center of rotation and is there when the motion is other than a straight line , even if the velocity is constant
Aa/Ab =( Wa^2 Ra)/ Wb^2Rb) = ( Wa^2/Wb^2 )(Rb/Ra)
= (1/3)^2 (1/3) = 1/27
The Frequency for circulaar motion is the inverse of the Period or Cycles/sec Fa =1/Ta =0.417 and Fb = 1/1.2 =0.833
The Velocity of a point on the cicumference of an object with circular motion is V= WR where W (Omega) is the angular velocity in Radians /sec and R is the radi;us.
The relationshio between the frequency and the angular velocity is F= W/2pi or W= 2pi F
Wa = 2 pi Fa =2.62 Rad/sec and Wb = 2 pi Fb = 5.24 Rad/sec
Va = Vb
Wa Ra = Wb Rb
Ra/Rb = Wb/Wa = 5.24/2.62 = 2
b ) If Ra/Rb = 3/1 what is the acceleration ratio Aa/Ab ?
The acceleration that applies here ils called Normal Acceleration An and equal to W^2R and is directed toward the center of rotation and is there when the motion is other than a straight line , even if the velocity is constant
Aa/Ab =( Wa^2 Ra)/ Wb^2Rb) = ( Wa^2/Wb^2 )(Rb/Ra)
= (1/3)^2 (1/3) = 1/27