A hollow, thin-walled sphere of mass 14.0 kg and diameter 45.0 cm is rotating ab

Question

A hollow, thin-walled sphere of mass 14.0 kg and diameter 45.0 cm 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 1.50.

A) What are the units of the constant A?

a) rad/s

b)rad/s2

c)rad/s3

d)rad/s4

B) What are the units of the constant B?

C) At the time 4.00 s , find the angular momentum of the sphere.

D) At the time 4.00 s , find the net torque on the sphere.

Explanation / Answer

3. Differentiate the equation
t = At^2+ Bt^4
angular momentum = 2t + [4 (Bt)] ^3 .....> after differentiation

now substitute the value t = 4 , B = 1.60

4. Differentiate again

Net torque = 0 + 12 (Bt)^2

for 1, 2 compare with a standard equation which might have been thought to you. Compare and you will get the units.

for eg. force on spring is F = k.x
where F - force,
k = spring constant
x = displacement

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