A hollow, thin-walled sphere of mass 11.0kg and diameter 41.0 cm is rotating abo

Question

A hollow, thin-walled sphere of mass 11.0kg and diameter 41.0 cm is rotating aboutan axle through its center. The angle (in radians) through which itturns as a function of time (in seconds) is given by (t) = At2 +Bt4, where A has numerical value 1.65and B has numerical value 1.09. (a) What are the units of the constantsA and B? A 1---Select---radrad/s^2rad/s B 2---Select---radrad/s^4rad/s^2
(b) At the time 3.00 s, find the following.
(i) the angular momentum of the sphere
3 kg · m2/s

(ii) the net torque on the sphere
4 N · m (t) = At2 +Bt4, (a) What are the units of the constantsA and B? A 1---Select---radrad/s^2rad/s B 2---Select---radrad/s^4rad/s^2
(b) At the time 3.00 s, find the following.
(i) the angular momentum of the sphere
3 kg · m2/s

(ii) the net torque on the sphere
4 N · m (i) the angular momentum of the sphere
3 kg · m2/s

(ii) the net torque on the sphere
4 N · m A 1---Select---radrad/s^2rad/s B 2---Select---radrad/s^4rad/s^2

Explanation / Answer

Given (t) = At2 + Bt4 where A = 1.65            B= 1.09 Unit of A = unit of / unit of t ^ 2               = rad / s ^ 2 Unit of B = unit of / unit of t^ 4              = rad / s ^ 4 (b)/ time t= 3 s mass m = 11 kg diameter d = 41 cm radius r= d / 2 = 20.5 cm = 0.205 m Angular momentum of the sphere L = I w where I = moment of inertia = ( 2/ 3) m r ^2             = 0.3081 kg m ^ 2 angular speed w = d / dt                          = 2At + 4Bt^3                          = ( 2*1.65*3) + ( 4 * 1.09* 3 ^ 3 )                          = 9.9 + 117.72 = 127.62 rad / s So, angular momentum L = 39.319 kg m ^ 2 / s (c). net torque T = I where = angular accleration = dw / dt                                              = 2A + 12B t^ 2                                              = 3.3 + 117.72                                              = 121.02 rad / s ^ 2 So, T = 37.286 N m where A = 1.65            B= 1.09 Unit of A = unit of / unit of t ^ 2               = rad / s ^ 2 Unit of B = unit of / unit of t^ 4              = rad / s ^ 4 (b)/ time t= 3 s mass m = 11 kg diameter d = 41 cm radius r= d / 2 = 20.5 cm = 0.205 m Angular momentum of the sphere L = I w where I = moment of inertia = ( 2/ 3) m r ^2             = 0.3081 kg m ^ 2 angular speed w = d / dt                          = 2At + 4Bt^3                          = ( 2*1.65*3) + ( 4 * 1.09* 3 ^ 3 )                          = 9.9 + 117.72 = 127.62 rad / s So, angular momentum L = 39.319 kg m ^ 2 / s (c). net torque T = I where = angular accleration = dw / dt                                              = 2A + 12B t^ 2                                              = 3.3 + 117.72                                              = 121.02 rad / s ^ 2 So, T = 37.286 N m

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