this is a rotational dynamics question on angular momemtum,inertia, and torque Q

Question

this is a rotational dynamics question on angular momemtum,inertia, and torque Q#2 (A) If a force of 4.0N is needed to open a 81cm wide door whenapplied at the edge opposite the hings, what force must be appliedwhen you push against the door10cm from the hinges side (B) A force of 303N is exerted on the end of a wrench in orderto appy a torque of 43.2NM to a bolt head. what angle does theforce make with respect to the wrench handle? (C) A wheel whose moment of inertia is 32kgm2 issubjected to a torqueof 12 NM. if the wheel is initiallymoving with an angular velocity of 6.0 rad/s when the torque isapplied, what will its angular velocity be if the torque is appliedfor 9.0s? (D) A toy airplane moves at the end of a string about a fixedpoint in a horizontal circle of 1.00m radius. if the linear speedis 4.86 m/s, what will the speed become if the string is pulled into give a radius of 0.750m? Assum there is no net torque this is a rotational dynamics question on angular momemtum,inertia, and torque Q#2 (A) If a force of 4.0N is needed to open a 81cm wide door whenapplied at the edge opposite the hings, what force must be appliedwhen you push against the door10cm from the hinges side (B) A force of 303N is exerted on the end of a wrench in orderto appy a torque of 43.2NM to a bolt head. what angle does theforce make with respect to the wrench handle? (C) A wheel whose moment of inertia is 32kgm2 issubjected to a torqueof 12 NM. if the wheel is initiallymoving with an angular velocity of 6.0 rad/s when the torque isapplied, what will its angular velocity be if the torque is appliedfor 9.0s? (D) A toy airplane moves at the end of a string about a fixedpoint in a horizontal circle of 1.00m radius. if the linear speedis 4.86 m/s, what will the speed become if the string is pulled into give a radius of 0.750m? Assum there is no net torque

Explanation / Answer

since torque is the same wehave r1 x F1=r2 x F2   since the force appliedis perpendicular to the door we have F2  = r1 F1 / r2 = 81 x4.0 / 10     F2  =32.4N (B) A force of 303N is exerted on theend of a wrench in order to appy a torque of 43.2NM to a bolt head.what angle does the force make with respect to the wrenchhandle? since = r x F = r F sin() = arcsin( / (rF) ) (C) A wheel whose moment ofinertia is 32kgm2 is subjected to a torqueof 12 NM. if thewheel is initially moving with an angular velocity of 6.0 rad/swhen the torque is applied, what will its angular velocity be ifthe torque is applied for 9.0s? Since = I then =/I and = (2 -1)/t 2 = t + 1 finally
2 = (/I) t + 1 2 = (12/32) 9.0 + 6.0 2 = 9.37 rad/s (D) A toy airplane moves at the end of astring about a fixed point in a horizontal circle of 1.00m radius.if the linear speed is 4.86 m/s, what will the speed become if thestring is pulled in to give a radius of 0.750m? Assum there is nonet torque Conservation of angular momentum is I11=I22   where1 = v1/R1 and2 = v2/R2 assuming the plane is a point mass of mass m I1=mR12 and similarlyI2=mR22 using I11=I22  we have mR12 v1/R1 =mR22 v2/R2 R1 v1 =R2v2 v2 =R1v1 /R2 v2 =1.00 x 4.86/0.75 v2 = 6.48m/s

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