Exam 8: Rotational Equilibrium and Rotational Dynamics: Part A

A meterstick is supported by a knife-edge at the 50-cm mark.Doug hangs masses of 0.40 and 0.60 kg from the 35-cm and 80-cm marks,respectively.Where should Doug hang a third mass of 0.30 kg to keep the stick balanced?

A 4.0-kg mass is placed at (3.0,4.0)m,and a 7.0 kg-mass is placed at (3.0,−4.0)m.What is the moment of inertia of this system of masses about the z axis?

A Ferris wheel starts at rest and builds up to a final angular speed of 0.70 rad/s while rotating through an angular displacement of 2.5 rad.What is its average angular acceleration?

A circular disk is rotating about a central axis with an angular velocity which is increasing at a constant rate.Point 1 on the disk is located at a distance From the center of the disk and point 2 on the disk is located at a distance From the center of the disk.If ,which of the following ratios is the largest? 1 and 2 refer to being at points 1 and 2 in the subscripts below,all values occurring at the same time.

A 0.12-m radius grinding wheel takes 2.1 s to speed up from 2.0 rad/s to 11.0 rad/s.What is the wheel's average angular acceleration?

Two children seat themselves on a seesaw.The one on the left has a weight of 400 N while the one on the right weighs 300 N.The fulcrum is at the midpoint of the seesaw.If the child on the right is not at the end but is 1.50 m from the fulcrum and the seesaw is balanced,what is the torque provided by the weight of the child on the left? (Take ccw as positive. )

A woman who weighs 500 N stands on an 8.0 m long board that weighs 100 N.The board is supported at each end.The support force at the right end is 2 times the support force at the left end.How far from the right end is the woman standing?

A bank vault is opened by applying a force of 300 N perpendicular to the plane of the door,1.2 m from the hinges.Find the torque due to this force about an axis through the hinges.

A baseball pitcher,loosening up his arm before a game,tosses a 0.15-kg ball using only the rotation of his forearm,0.32 m in length,to accelerate the ball.If the ball starts at rest and is released with a speed of 24 m/s in a time of 0.40 s,what is the average angular acceleration of the arm and ball?

Which of the first units given below can be units for angular acceleration while the second units can be units for angular velocity?

A spool of thread has an average radius of 1.00 cm.If the spool contains 126 m of thread,how many turns of thread are on the spool? "Average radius" allows us to not need to treat the layering of threads on lower layers.

A uniform rod of length L and weight W is placed on a fulcrum a distance of 0.4L from the left end.On the left end is placed a mass of weight 2W and on the right end a vertical force F is applied to keep the system in balance.What are the magnitude and direction of the force F?

A 0.40-m radius automobile tire accelerates from rest at a constant 2.0 rad/s².What is the centripetal acceleration of a point on the outer edge of the tire after 5.0 s?

A bucket filled with water has a mass of 23 kg and is attached to a rope,which in turn,is wound around a 0.080-m radius cylinder at the top of a well.What torque does the weight of water and bucket produce on the cylinder if the cylinder is not permitted to rotate? (g = 9.8 m/s²)

A baseball pitcher loosens up his pitching arm.He tosses a 0.20-kg ball using only the rotation of his forearm,0.32 m in length,to accelerate the ball.What is the moment of inertia of the ball alone as it moves in a circular arc with a radius of 0.32 m?

A 0.200-kg object is swung in a circular path and in a vertical plane on a 0.500-m length string.If the angular speed at the bottom is 8.00 rad/s,what is the tension in the string when the object is at the bottom of the circle?

A non-uniform rod of length L and mass M is pivoted about one end.The moment of inertia of this rod about its pivoted end is )Attached to the rod is a mass M at its midpoint and at the end opposite the pivot is another mass 2M.What is the moment of inertia of this configuration about the pivot?

A 4.0-kg mass is placed at (3.0,4.0)m,and a 7.0-kg mass is placed at (3.0,−4.0)m.What is the moment of inertia of this system of masses about the x axis?

An 80-kg man is one fourth of the way up a 10-m ladder that is resting against a smooth,frictionless wall.If the ladder has a mass of 30 kg and it makes an angle of 60° with the ground,find the force of friction of the ground on the foot of the ladder.

A bucket in an old well is hoisted upward by a rope which winds up on a cylinder having a radius of 0.050 m.How many rev/s must the cylinder turn if the bucket is raised at a speed of 0.20 m/s?