Question 1

A 8.4-kg mass is placed at (4.0,5.0)m.Where can a 4.2-kg mass be placed so that the moment of inertia about the z axis is zero?

Accepted Answer

The moment of inertia cannot be zero for a non-zero mass distribution about an axis, as it depends on the mass and its distance from the axis.

Question 2

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?

Accepted Answer

The moment of inertia of a point mass is given by:
I=mr^2
where:
m = mass of the ball
r = radius of the circular arc

We are given the mass of the ball as 0.20 kg and the radius of the circular arc as 0.32 m. Substituting these values into the equation above, we get:

I = (0.20 kg) x (0.32 m)^2 = 0.02048 kg·m^2

Rounding this off to two significant figures, we get:
I = 1.9 x 10^-2 kg·m^2

Thus, the best choice is B.

Question 3

A uniform rod of length L and weight W is placed on a fulcrum a distance of 0.2L from the left end.On the left end is placed a mass of weight 3W 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?
​

Accepted Answer

The first step is to find the distance between the right end and the fulcrum. Since the fulcrum is 0.2L from the left end, the distance between the right end and the fulcrum is 0.8L. We can then use the principle of moments to solve for F. The clockwise moment (due to the weight of the rod) is W(0.5L), and the counterclockwise moments are 3W(L) and F(0.8L). For the system to be in balance, the moments must be equal, so we have:
W(0.5L) = 3W(L) + F(0.8L)
Simplifying and solving for F, we get:
F = (0.5W/0.8L)(L) = 0.625W
Since the weight is pulling down, the force F must pull up to balance the system, so the answer is 0.625W, up. Choice C is the only one that matches this answer.

Question 4

An object consists of a rod (of length 4.0 m and negligible moment of inertia)to which five small 2.0-kg masses are attached,one at each end and one at each point on the rod 1.0 m from each end.(The masses are one meter apart. )The moment of inertia of this object about an axis perpendicular to the rod and through one of the end masses:

Accepted Answer

The moment of inertia is calculated by summing $ m \times r^2 $ for each mass, where $ m = 2 \, \text{kg} $ and $ r $ is the distance from the axis. The distances are 0 m, 1 m, 2 m, 3 m, and 4 m, resulting in $ 2(0^2) + 2(1^2) + 2(2^2) + 2(3^2) + 2(4^2) = 60 \, \text{kg} \cdot \text{m}^2 $.

Question 5

A 4.0-kg mass is placed at (2.0,3.0)m,and a 7.0-kg mass is placed at (2.0,−3.0)m.What is the moment of inertia of this system of masses about the y axis?

Accepted Answer

The moment of inertia about the y-axis is calculated using I = Σm*x². For the 4.0-kg mass at (2.0,3.0)m, I = 4.0*(2.0)² = 16 kg·m². For the 7.0-kg mass at (2.0,-3.0)m, I = 7.0*(2.0)² = 28 kg·m². Total I = 16 + 28 = 44 kg·m².

Question 6

A woman who weighs 500 N stands on an 8.0 m long board that weighs 200 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?

Accepted Answer

The answer of A woman who weighs 500 N stands...

Question 7

A meterstick is supported by a knife-edge at the 50-cm mark.Doug hangs masses of 0.40 and 0.80 kg from the 15-cm and 80-cm marks,respectively.Where should Doug hang a third mass of 0.20 kg to keep the stick balanced?

Accepted Answer

The answer of A meterstick is supported by a knife-edge...

Question 8

A uniform,horizontal beam of length 8.0 m and weight 14 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° with the horizontal.What is the tension in the cable needed to maintain the beam in equilibrium?

Accepted Answer

The answer of A uniform,horizontal beam of length 8.0 m...

Question 9

A 300-N uniform ladder,8.0 m long,rests against a smooth vertical wall.The coefficient of static friction between ladder and floor is 0.30.What minimum angle can the ladder make with the floor before it slips?

Accepted Answer

The minimum angle can be found using the formula for static friction and the conditions for equilibrium. The frictional force must equal the component of the ladder's weight parallel to the floor. Using trigonometry and the given coefficient of static friction, the minimum angle is calculated to be approximately 59°.

Question 10

Two hoops or rings (I = MR²)are centered,lying on a turntable.The smaller ring has radius = 0.05 m;the larger has radius = 0.1 m.Both have a mass of 6.0 kg.What is the total moment of inertia as the turntable spins? Ignore the mass of the turntable.

Accepted Answer

The answer of Two hoops or rings (I = MR²)are...

Question 11

A bucket of water with total mass 25 kg is attached to a rope,which in turn is wound around a 0.04-m radius cylinder at the top of a well.The bucket is raised to the top of the well and released.The bucket is moving with a speed of 5.0 m/s upon hitting the water surface in the well.What is the angular speed of the cylinder at this instant?

Accepted Answer

The answer of A bucket of water with total mass...

Question 12

An 700-N billboard worker stands on a 5.0-m scaffold weighing 500 N and supported by vertical ropes at each end.How far would the worker stand from one of the supporting ropes to produce a tension of 780 N in that rope?

Accepted Answer

The answer of An 700-N billboard worker stands on a...

Question 13

A bowling ball has a mass of 9.0 kg,a moment of inertia of 3.6 × 10−² kg·m²,and a radius of 0.10 m.If it rolls down the lane without slipping at a linear speed of 3 m/s,what is its angular speed?

Accepted Answer

The angular speed ω can be found using the relationship v = ωr, where v is the linear speed and r is the radius. Thus, ω = v/r = 3 m/s / 0.10 m = 30 rad/s.

Question 14

A 0.40-m radius automobile tire rotates how many rad after starting from rest and accelerating at a constant 2.0 rad/s² over a 6.0-s interval?

Accepted Answer

The answer of A 0.40-m radius automobile tire rotates how...

Question 15

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 3 
)Attached to the rod is a mass M at its midpoint and at the end opposite the pivot is another mass 3M.What is the moment of inertia of this configuration about the pivot?

Accepted Answer

The answer of A non-uniform rod of length L and...

Question 16

A 3.0-kg mass is placed at (4.0,5.0)m,and a 6.0-kg mass is placed at (4.0,−5.0)m.What is the moment of inertia of this system of masses about the z axis?

Accepted Answer

The moment of inertia about the z-axis is calculated using I = Σm*r², where r is the distance from the axis. For the 3.0-kg mass, r = 5.0 m, and for the 6.0-kg mass, r = 5.0 m. Thus, I = 3.0*(5.0)² + 6.0*(5.0)² = 75 + 150 = 225 kg·m².

Question 17

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

Accepted Answer

The answer of A uniform rod of length L and...

Question 18

A majorette takes two batons and fastens them together in the middle at right angles to make an "x" shape.Each baton was 0.90 m long and each ball on the end is 0.20 kg.(Ignore the mass of the rods. )What is the moment of inertia if the arrangement is spun around an axis through the center perpendicular to both rods?

Accepted Answer

The moment of inertia for each ball is calculated using I = mr², where m is the mass and r is the distance from the axis. Each ball is 0.45 m from the center (half of 0.90 m). So, I for one ball = 0.20 kg * (0.45 m)² = 0.0405 kg·m². There are four balls, so total I = 4 * 0.0405 kg·m² = 0.162 kg·m².

Question 19

A 3.0-kg mass is placed at (2.0,3.0)m,and a 6.0-kg mass is placed at (2.0,−3.0)m.What is the moment of inertia of this system of masses about the x axis?

Accepted Answer

The answer of A 3.0-kg mass is placed at (2.0,3.0)m,and...

Question 20

A majorette takes two batons and fastens them together in the middle at right angles to make an "x" shape.Each baton was 0.60 m long and each ball on the end is 0.10 kg.(Ignore the mass of the rods. )What is the moment of inertia if the arrangement is spun around an axis formed by one of the batons?

Accepted Answer

The moment of inertia of a rod about an axis through its center perpendicular to the rod is (1/12)ML^2. The moment of inertia of a point mass about an axis is mr^2. The moment of inertia of the arrangement about an axis formed by one of the batons is:I = (1/12)(0.10 kg)(0.60 m)^2 + (0.10 kg)(0.60 m)^2 + (0.10 kg)(0.60 m)^2 = 0.018 kg·m^2

Quiz 8: Rotational Equilibrium and Rotational Dynamics

A 8.4-kg mass is placed at (4.0,5.0) m.Where can a 4.2-kg mass be placed so that the moment of inertia about the z axis is zero?

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 uniform rod of length L and weight W is placed on a fulcrum a distance of 0.2L from the left end.On the left end is placed a mass of weight 3W 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 4.0-kg mass is placed at (2.0,3.0) m,and a 7.0-kg mass is placed at (2.0,−3.0) m.What is the moment of inertia of this system of masses about the y axis?

A woman who weighs 500 N stands on an 8.0 m long board that weighs 200 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 meterstick is supported by a knife-edge at the 50-cm mark.Doug hangs masses of 0.40 and 0.80 kg from the 15-cm and 80-cm marks,respectively.Where should Doug hang a third mass of 0.20 kg to keep the stick balanced?

A 300-N uniform ladder,8.0 m long,rests against a smooth vertical wall.The coefficient of static friction between ladder and floor is 0.30.What minimum angle can the ladder make with the floor before it slips?

Two hoops or rings (I = MR²) are centered,lying on a turntable.The smaller ring has radius = 0.05 m;the larger has radius = 0.1 m.Both have a mass of 6.0 kg.What is the total moment of inertia as the turntable spins? Ignore the mass of the turntable.

An 700-N billboard worker stands on a 5.0-m scaffold weighing 500 N and supported by vertical ropes at each end.How far would the worker stand from one of the supporting ropes to produce a tension of 780 N in that rope?

A bowling ball has a mass of 9.0 kg,a moment of inertia of 3.6 × 10−² kg·m²,and a radius of 0.10 m.If it rolls down the lane without slipping at a linear speed of 3 m/s,what is its angular speed?

A 0.40-m radius automobile tire rotates how many rad after starting from rest and accelerating at a constant 2.0 rad/s² over a 6.0-s interval?

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 3 ) Attached to the rod is a mass M at its midpoint and at the end opposite the pivot is another mass 3M.What is the moment of inertia of this configuration about the pivot?

A 3.0-kg mass is placed at (4.0,5.0) m,and a 6.0-kg mass is placed at (4.0,−5.0) m.What is the moment of inertia of this system of masses about the z axis?

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

A 3.0-kg mass is placed at (2.0,3.0) m,and a 6.0-kg mass is placed at (2.0,−3.0) m.What is the moment of inertia of this system of masses about the x axis?

Quiz 8: Rotational Equilibrium and Rotational Dynamics

A 8.4-kg mass is placed at (4.0,5.0) m.Where can a 4.2-kg mass be placed so that the moment of inertia about the z axis is zero?

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 uniform rod of length L and weight W is placed on a fulcrum a distance of 0.2L from the left end.On the left end is placed a mass of weight 3W 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 4.0-kg mass is placed at (2.0,3.0) m,and a 7.0-kg mass is placed at (2.0,−3.0) m.What is the moment of inertia of this system of masses about the y axis?

A woman who weighs 500 N stands on an 8.0 m long board that weighs 200 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 meterstick is supported by a knife-edge at the 50-cm mark.Doug hangs masses of 0.40 and 0.80 kg from the 15-cm and 80-cm marks,respectively.Where should Doug hang a third mass of 0.20 kg to keep the stick balanced?

A 300-N uniform ladder,8.0 m long,rests against a smooth vertical wall.The coefficient of static friction between ladder and floor is 0.30.What minimum angle can the ladder make with the floor before it slips?

Two hoops or rings (I = MR2) are centered,lying on a turntable.The smaller ring has radius = 0.05 m;the larger has radius = 0.1 m.Both have a mass of 6.0 kg.What is the total moment of inertia as the turntable spins? Ignore the mass of the turntable.

An 700-N billboard worker stands on a 5.0-m scaffold weighing 500 N and supported by vertical ropes at each end.How far would the worker stand from one of the supporting ropes to produce a tension of 780 N in that rope?

A bowling ball has a mass of 9.0 kg,a moment of inertia of 3.6 × 10−2 kg·m2,and a radius of 0.10 m.If it rolls down the lane without slipping at a linear speed of 3 m/s,what is its angular speed?

A 0.40-m radius automobile tire rotates how many rad after starting from rest and accelerating at a constant 2.0 rad/s2 over a 6.0-s interval?

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 3 ) Attached to the rod is a mass M at its midpoint and at the end opposite the pivot is another mass 3M.What is the moment of inertia of this configuration about the pivot?

A 3.0-kg mass is placed at (4.0,5.0) m,and a 6.0-kg mass is placed at (4.0,−5.0) m.What is the moment of inertia of this system of masses about the z axis?

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

A 3.0-kg mass is placed at (2.0,3.0) m,and a 6.0-kg mass is placed at (2.0,−3.0) m.What is the moment of inertia of this system of masses about the x axis?

A uniform rod of length L and weight W is placed on a fulcrum a distance of 0.2L from the left end.On the left end is placed a mass of weight 3W 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?

Two hoops or rings (I = MR²) are centered,lying on a turntable.The smaller ring has radius = 0.05 m;the larger has radius = 0.1 m.Both have a mass of 6.0 kg.What is the total moment of inertia as the turntable spins? Ignore the mass of the turntable.

A bowling ball has a mass of 9.0 kg,a moment of inertia of 3.6 × 10−² kg·m²,and a radius of 0.10 m.If it rolls down the lane without slipping at a linear speed of 3 m/s,what is its angular speed?

A 0.40-m radius automobile tire rotates how many rad after starting from rest and accelerating at a constant 2.0 rad/s² over a 6.0-s interval?