An object with a mass of # 2 kg# is traveling in a circular path of a radius of #4 m#. If the object's angular velocity changes from # 1 Hz# to # 12 Hz# in # 2 s#, what torque was applied to the object?

1 Answer
Jun 4, 2016

Answer:

#T=352pi " "N*m#

Explanation:

#m=2" "kg" mass of object"#

#r=4" "m " radius of the circular path"#

#f_1=1" "Hz" initial frequency of object"#

#f_2=12" "Hz" final frequency of object"#

#Delta t=2" "s#

#F=m*a " Newton equation for linear motion"#

#T=I*alpha" Newton equation for rotary motion"#

#T " represents Torque of object"#

#I " represents the moment of inertia of the object"#

#alpha " represents angular acceleration of the object"#

#alpha=(omega_2-omega_1)/(Delta t)#

#"the angular velocity of an object is expressed as "omega=2*pi*f#

#alpha=(2*pi(f_2-f_1))/2=pi(f_2-f_1)=pi(12-1)=11pi#

#I=m*r^2=2*4^2=32#

#T=32*11pi#

#T=352pi " "N*m#