Rigid Body Newtonian Mechanics - Review Problems

RP6-1) What is the difference between a body's centroid, and the center of gravity? Select the quantity that matches the definition.

• A body's center of volume.         

 

• A body's average location of mass.         

 

• A body's average location of the gravitational force.         

 

• The centroid and center of mass are always located in the same location.        

 

• The center of mass and the center of gravity are always located in the same location.        

 

RP6-2) What is the difference between a body's area moment of inertia and a body's mass moment of inertia? Select the quantity that matches the definition.

• A measure of a body’s resistance to angular acceleration about a given axis.       

 

• A measure of a body’s resistance to bending about a given axis.       

 

• The area moment of inertia and mass moment of inertia are both identified by the variable I.        

 

• The area moment of inertia and the mass moment of inertia always have the same value.        

 

RP6-3) Explain the physical significance of the r_G/P x ma_P term in the moment equation ∑M_P = r_G/P x ma_P as employed for the case of pure translation.

RP6-4) One form of Euler’s second law states that ∑M_O = I_Oα . What must be true about point O for this equation to hold true? Check all that apply.

RP6-5) The forklift shown is carrying a load of sand bags weighing 700 lb. The forklift itself weighs 5000 lb. Determine the maximum safe upward acceleration of the load if the forklift is not moving and when the forklift is moving forward with an acceleration of 5 m/s². The forklift dimensions are as follows: c = 2 m, b = 1 m, d = 1.7 m, h = 1.5 m and h_L = 5 m.

RP6-6) The articulating robot arm shown has a total of 4 motors controlling each joint. Determine the minimum size required (in terms of torque) of the motor controlling the 2nd axis if it is desired that the end affecter (approximated as joint 4) is capable of reaching a speed of 1 m/s from rest in 1 second in a straight-arm position (i.e. the arms are in line and the motors at the 3rd and 4th joint are not being operated). The arm parameters are as follows: m_arm1 = 25 kg, m_arm2 = 15 kg, L_arm1 = 1.5 m, L_arm2 = 2 m, and the mass of the motors controlling the 3rd and 4th axes are m_m3 = 3 kg and m_m4 = 2 kg, respectively. You may assume that each arm is a slender rod and that each motor is a particle. Note that the highest demand on the 2nd axis motor will be when all sections of the arm are horizontal.

RP6-7) A 15-inch car tire starting from rest rolls down a 30^o ramp. How long will it take for the tire's center to travel 20 meters along the ramp? The coefficients of static and kinetic friction are μ_s = 0.9 and μ_k = 0.6, respectively. The tire's radius of gyration about its center is 1.2 ft.

Is the no-slip assumption valid?

RP6-8) A slender bar (m = 9 kg, L = 2 m) rests on a smooth block of ice. A force (F) is applied at a distance d = 0.75 m from the center of mass (G) in the direction shown. The resulting acceleration of point A (the point where the force is applied) at this instant is 1 m/s². Determine the acceleration of point B and the magnitude of force F required to generate this motion.

Which reference point should be used?