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 # 9 Hz# in # 3 s#, what torque was applied to the object?

1 Answer
Jan 2, 2016

Answer:

Use basic rotational motion mechanics.

#τ=536.2 N*m#

Explanation:

The angular acceleration is:

#a=(Δω)/(Δt)#

#a=(9-1)/3 ((rounds)/s)/s#

#a=8/3 (rounds)/s^2#

Or in rads:

#a=8/3*2π#

#a=(16π)/3(rad)/s^2#

The moment of inertia of the object is:

#I=m*r^2#

#I=2*4^2 kg*m^2#

#I=32 kg*m^2#

Finally, the torque is calculated:

#τ=I*a#

#τ=32*(16π)/3 kg*m^2*1/s^2#

#τ=536.2 (kg*m/s^2)*m#

#τ=536.2 N*m#