A hollow, thin-walled sphere of mass 13.0kg and diameter 47.0cm is rotating abou

Question

A hollow, thin-walled sphere of mass 13.0kg and diameter 47.0cm is rotating about an axle through its center. The angle (in radians) through which it turns as a function of time (in seconds) is given by ?(t)=At2+Bt4, where A has numerical value 1.10 and B has numerical value 1.60.

Part A

What are the units of the constant A?

Part B

What are the units of the constant B?

Part C

At the time 3.00s , find the angular momentum of the sphere.

Part D

At the time 3.00s , find the net torque on the sphere.

Explanation / Answer

A) it has to rad s^-2 since A*t^2= rad.so, A= rad s^-2

B) B*s^4 = rad.

or B= rad s^-4

c) w(t)=2At + 4Bt^3

w(3) = 2*1.1*3 + 4*1.6*3^3

=179.4 rad/s

so momentum = Iw

=(2/3)*13* (0.47*0.5)^2 * 179.4

=85.86

D) alpha = d^2w/dt^2

=2A + 12 Bt^2

=2*1.1 + 12*1.6*3^2

=175 rad/s^2

so torque= I*alpha

=175*(2/3)*13*(0.5*0.47)^2

=83.758 Nm

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