The graph describes the angular momentum of an object as a function of time. The

Question

The graph describes the angular momentum of an object as a function of time. The object
has a moment of inertia of 65kgm^2 about the axis of rotation.

a) What is the angular velocity of the object when t = 5.5 seconds?
b) Calculate the average torque acting on the object between t = 3.5 and t = 5.5 seconds?
c) Estimate the angular displacement of the object between t = 6 and t = 7 seconds?

The graph describes the angular momentum of an object as a function of time. The object has a moment of inertia of 65kgm^2 about the axis of rotation. What is the angular velocity of the object when t = 5.5 seconds? Calculate the average torque acting on the object between t = 3.5 and t = 5.5 seconds? Estimate the angular displacement of the object between t = 6 and t = 7 seconds?

Explanation / Answer

I = 65 kg.m^2

a)

at t = 5.5 s

L = 900 kg.m^2/s

L = I*w

==> w = L/I = 900/65 = 13.85 rad/s

b)

T = (L2-L1)/(t2-t1)

= (900-100)/(5.5-3.5)

= -50 N.m

c)

at t = 6s, L = 600 kg.m^2/s

w = L/I = 600/65 = 9.23 rad/s

T = (L2-L1)/(t2-t1)

= (-550-600)/(7-6)

= -1150 N.m


alfa = T/I = -1150/65 = -17.69 rad/s^2


now

angular displacement, theta = w*t + 0.5*alfa*t^2

theta = 9.23*1 - 0.5*17.69*1^2

= 0.385 radians

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