Question 1

A bucket of water with total mass 21.0 kg is attached to a rope,which in turn is wound around a 0.050-m radius cylinder,with crank,at the top of a well.The moment of inertia of the cylinder and crank is 0.21 kg 
M2.The bucket is raised to the top of the well and released to fall back into the well.What is the kinetic energy of the cylinder and crank at the instant the bucket is moving with a speed of 5.4 m/s?

Accepted Answer

A) 4.8E+2 J 
B) 1.2E+3 J 
C) 3.1E+2 J 
D) 1.2E+4 J

Question 2

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 0.250 m/s?

Accepted Answer

A) 5.00 rev/s 
B) 7.85 rev/s 
C) 1.59 rev/s 
D) 0.80 rev/s 
E) 3.18 rev/s

Question 3

A uniform solid sphere rolls down an incline of height 3 m after starting from rest.In order to calculate its speed at the bottom of the incline,one needs to know:

Accepted Answer

A) the mass of the sphere. 
B) the radius of the sphere. 
C) the mass and the radius of the sphere. 
D) no more than is given in the problem.

Question 4

A baseball pitcher loosens up his pitching arm.He tosses a 0.20-kg ball using only the rotation of his forearm,0.28 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 0.28 m?

Accepted Answer

A) 3.1E-3 kg·m2 
B) 1.6E-2 kg·m2 
C) 3.1E-2 kg·m2 
D) 1.1E-2 kg·m2 
E) 5.6E-2 kg·m2

Question 5

A 40-kg boy is standing on the edge of a stationary 30-kg circular platform that is free to rotate.The boy tries to walk around the platform in a counterclockwise direction.As he does:

Accepted Answer

A) the platform doesn't rotate. 
B) the platform rotates in a clockwise direction just fast enough so that the boy remains stationary relative to the ground. 
C) the platform rotates in a clockwise direction while the boy goes around in a counterclockwise direction relative to the ground. 
D) both go around with equal angular velocities but in opposite directions.

Question 6

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 1ML2/4.Attached to the rod is a mass 3M 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?

Accepted Answer

A) 3ML2 
B) 2ML2 
C) 4ML2 
D) 5ML2 
E) None of the above answers is correct.

Question 7

An object with mass m and moment of inertia I is spinning with an angular momentum L.Its kinetic energy is:

Accepted Answer

A) 0.5I2/L. 
B) 0.5L2/I. 
C) 0.5L2/m. 
D) 0.5I2/m.

Question 8

A 3.00-m rod is pivoted about its left end.A force of 7.80 N is applied perpendicular to the rod at a distance of 1.60 m from the pivot causing a ccw torque,and a force of 2.60 N is applied at the end of the rod 3.00 m from the pivot.The 2.60-N force is at an angle of 30.0o to the rod and causes a cw torque.What is the net torque about the pivot? (Take ccw as positive. )

Accepted Answer

A) 16.4 N·m 
B) -8.58 N·m 
C) 8.58 N·m 
D) -16.4 N·m 
E) 4.68 N·m

Question 9

A bus is designed to draw its power from a rotating flywheel that is brought up to its maximum speed (3000 rpm)by an electric motor.The flywheel is a solid cylinder of mass 250 kg and radius 0.500 m (Icylinder = MR2/2).If the bus requires an average power of 10.0 kW,how long will the flywheel rotate?

Accepted Answer

A) 154 s 
B) 308 s 
C) 463 s 
D) 617 s

Question 10

A system of 3 masses is located as follows: m1 = m0 at (0,L),m2 = 2m0 at the origin,and m3 = 3m0 at (3L,0).Where is the center of mass of these masses?

Accepted Answer

A)   
B)   
C)   
D)

Question 11

A woman who weighs 500 N stands on a 6.0-m-long board that weighs 100 N.The board is supported at each end.The support force at the right end is 3 times the support force at the left end.How far from the right end is the woman standing?

Accepted Answer

A) 4.8 m 
B) 2.1 m 
C) 1.7 m 
D) 1.2 m 
E) ​3.9 m

Question 12

Three masses are positioned along the x-axis.Their masses and positions are m1 = m with x1 = 1.0 m,m2 = 2m with x2 = 2.0 m,and m3 = 9.0m with x3 = 3.0 m.What is the x-coordinate of the center of mass of this system,to the nearest tenth?

Accepted Answer

A) 4.7 m 
B) 2.7 m 
C) 2.0 m 
D) 0.7 m 
E) Not enough information

Question 13

A uniform,horizontal beam of length 8.0 m and weight 42.4 N is attached at one end to a wall by a pin connection (so that it may rotate).A cable attached to the wall above the pin supports the opposite end.The cable makes an angle of 60.0° with the horizontal.What is the tension in the cable needed to maintain the beam in equilibrium?

Accepted Answer

A) 24.5 N 
B) 49.0 N 
C) 294 N 
D) 4.59 N 
E) 171 N

Question 14

A rod system with a uniform linear density of $\lambda$ = 4.40 kg/m has the shape shown in the figure,with rod 1 the vertical rod and rod 2 the horizontal rod.Rod 1 has length LS1U1B11S1U1B0 = 8.00 m,and rod 2 has length LS1U1B12S1U1B0 = 7.50 m.Neglect the diameter of the rods.  ​
-What is the center of mass of the system?

Accepted Answer

A) (1.29 m,3.31 m) 
B) (2.06 m,3.10 m) 
C) (3.31 m,1.29 m) 
D) (3.10 m,2.06 m)

Question 15

A rotating flywheel can be used as a method to store energy.If it is required that such a device be able to store up to a maximum of 2.00 × 106 J when rotating at 400 rad/s,what moment of inertia is required?

Accepted Answer

A) 50.0 kg  m2 
B) 25.0 kg  m2 
C) 12.5 kg  m2 
D) 6.30 kg  m2

Question 16

A uniform meterstick balances on a fulcrum placed at the 70.0-cm mark when a weight w is placed at the 90.0-cm mark.What is the weight of the meterstick?

Accepted Answer

A) w 
B) 1.0w 
C) w/1.0 
D) 0.70w 
E) 0.90w

Question 17

An object of radius R and moment of inertia I rolls down an incline of height H after starting from rest.Its total kinetic energy at the bottom of the incline:

Accepted Answer

A) is gR/I. 
B) is I/gH. 
C) is 0.5Ig/H. 
D) cannot be found from the given information alone.

Question 18

A solid sphere,a solid cylinder,and a hoop each have the same mass and radius.If they are spinning at the same angular velocity,which one has the greatest angular momentum?

Accepted Answer

A) the sphere 
B) the cylinder 
C) the hoop 
D) They all have the same angular momentum.

Question 19

A disk has a moment of inertia of 3.0 × 10−4 kg·m2 and rotates with an angular speed of 3.6 rad/s.What net torque must be applied to bring it to rest within 3.6 s?

Accepted Answer

A) 3.89E-4 N·m. 
B) 3.00E-4 N·m 
C) 4.32E-4 N·m 
D) 3.00E-4 N·m. 
E) 1.20E-4 N·m

Question 20

A solid sphere of mass 2.50 kg and radius 0.120 m is at rest at the top of a ramp inclined 15.0°.It rolls to the bottom without slipping.The upper end of the ramp is 1.20 m higher than the lower end.Find the sphere's total kinetic energy when it reaches the bottom.

Accepted Answer

A) 70.0 J 
B) 47.9 J 
C) 29.4 J 
D) 8.80 J

Exam 8: Rotational Equilibrium and Dynamics

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 0.250 m/s?

A uniform solid sphere rolls down an incline of height 3 m after starting from rest.In order to calculate its speed at the bottom of the incline,one needs to know:

A baseball pitcher loosens up his pitching arm.He tosses a 0.20-kg ball using only the rotation of his forearm,0.28 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 0.28 m?

A 40-kg boy is standing on the edge of a stationary 30-kg circular platform that is free to rotate.The boy tries to walk around the platform in a counterclockwise direction.As he does:

An object with mass m and moment of inertia I is spinning with an angular momentum L.Its kinetic energy is:

A system of 3 masses is located as follows: m₁ = m₀ at (0,L) ,m₂ = 2m₀ at the origin,and m₃ = 3m₀ at (3L,0) .Where is the center of mass of these masses?

A woman who weighs 500 N stands on a 6.0-m-long board that weighs 100 N.The board is supported at each end.The support force at the right end is 3 times the support force at the left end.How far from the right end is the woman standing?

Three masses are positioned along the x-axis.Their masses and positions are m₁ = m with x₁ = 1.0 m,m₂ = 2m with x₂ = 2.0 m,and m₃ = 9.0m with x₃ = 3.0 m.What is the x-coordinate of the center of mass of this system,to the nearest tenth?

A rotating flywheel can be used as a method to store energy.If it is required that such a device be able to store up to a maximum of 2.00 × 10⁶ J when rotating at 400 rad/s,what moment of inertia is required?

A uniform meterstick balances on a fulcrum placed at the 70.0-cm mark when a weight w is placed at the 90.0-cm mark.What is the weight of the meterstick?

An object of radius R and moment of inertia I rolls down an incline of height H after starting from rest.Its total kinetic energy at the bottom of the incline:

A solid sphere,a solid cylinder,and a hoop each have the same mass and radius.If they are spinning at the same angular velocity,which one has the greatest angular momentum?

A disk has a moment of inertia of 3.0 × 10−⁴ kg·m² and rotates with an angular speed of 3.6 rad/s.What net torque must be applied to bring it to rest within 3.6 s?

A solid sphere of mass 2.50 kg and radius 0.120 m is at rest at the top of a ramp inclined 15.0°.It rolls to the bottom without slipping.The upper end of the ramp is 1.20 m higher than the lower end.Find the sphere's total kinetic energy when it reaches the bottom.

Exam 8: Rotational Equilibrium and Dynamics

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 0.250 m/s?

A uniform solid sphere rolls down an incline of height 3 m after starting from rest.In order to calculate its speed at the bottom of the incline,one needs to know:

A baseball pitcher loosens up his pitching arm.He tosses a 0.20-kg ball using only the rotation of his forearm,0.28 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 0.28 m?

A 40-kg boy is standing on the edge of a stationary 30-kg circular platform that is free to rotate.The boy tries to walk around the platform in a counterclockwise direction.As he does:

An object with mass m and moment of inertia I is spinning with an angular momentum L.Its kinetic energy is:

A system of 3 masses is located as follows: m1 = m0 at (0,L) ,m2 = 2m0 at the origin,and m3 = 3m0 at (3L,0) .Where is the center of mass of these masses?

A woman who weighs 500 N stands on a 6.0-m-long board that weighs 100 N.The board is supported at each end.The support force at the right end is 3 times the support force at the left end.How far from the right end is the woman standing?

Three masses are positioned along the x-axis.Their masses and positions are m1 = m with x1 = 1.0 m,m2 = 2m with x2 = 2.0 m,and m3 = 9.0m with x3 = 3.0 m.What is the x-coordinate of the center of mass of this system,to the nearest tenth?

A rotating flywheel can be used as a method to store energy.If it is required that such a device be able to store up to a maximum of 2.00 × 106 J when rotating at 400 rad/s,what moment of inertia is required?

A uniform meterstick balances on a fulcrum placed at the 70.0-cm mark when a weight w is placed at the 90.0-cm mark.What is the weight of the meterstick?

An object of radius R and moment of inertia I rolls down an incline of height H after starting from rest.Its total kinetic energy at the bottom of the incline:

A solid sphere,a solid cylinder,and a hoop each have the same mass and radius.If they are spinning at the same angular velocity,which one has the greatest angular momentum?

A disk has a moment of inertia of 3.0 × 10−4 kg·m2 and rotates with an angular speed of 3.6 rad/s.What net torque must be applied to bring it to rest within 3.6 s?

A solid sphere of mass 2.50 kg and radius 0.120 m is at rest at the top of a ramp inclined 15.0°.It rolls to the bottom without slipping.The upper end of the ramp is 1.20 m higher than the lower end.Find the sphere's total kinetic energy when it reaches the bottom.

A system of 3 masses is located as follows: m₁ = m₀ at (0,L) ,m₂ = 2m₀ at the origin,and m₃ = 3m₀ at (3L,0) .Where is the center of mass of these masses?

Three masses are positioned along the x-axis.Their masses and positions are m₁ = m with x₁ = 1.0 m,m₂ = 2m with x₂ = 2.0 m,and m₃ = 9.0m with x₃ = 3.0 m.What is the x-coordinate of the center of mass of this system,to the nearest tenth?

A rotating flywheel can be used as a method to store energy.If it is required that such a device be able to store up to a maximum of 2.00 × 10⁶ J when rotating at 400 rad/s,what moment of inertia is required?

A disk has a moment of inertia of 3.0 × 10−⁴ kg·m² and rotates with an angular speed of 3.6 rad/s.What net torque must be applied to bring it to rest within 3.6 s?