Question 1

The torque caused by a force F applied at a distance r from the axis of rotation,is given by τ = rF​sinθ,where θ is the angle between 
And 
)If the magnitudes r and F remain the same,what other angle θ' will produce the same torque as was produced at angle θ if θ was less than 90°?

Accepted Answer

Since sin(θ) = sin(180 - θ), we can use the same values of r and F for both angles if we use θ' = 180 - θ. Therefore, the torque produced will be the same.

Question 2

A bucket of water with total mass 23 kg is attached to a rope,which in turn,is wound around a 0.080-m radius cylinder at the top of a well.A crank with a turning radius of 0.25 m is attached to the end of the cylinder.What minimum force directed perpendicular to the crank handle is required to just raise the bucket? (Assume the rope's mass is negligible,that the cylinder turns on frictionless bearings,and that g = 9.8 m/s². )

Accepted Answer

The force required to just raise the bucket can be found by calculating the minimum force needed to counteract the weight of the bucket.

Weight of bucket = mass x acceleration due to gravity 
= 23 kg x 9.8 m/s^2 = 225.4 N

The force needed to just raise the bucket can be found using the torque equation:

Torque = force x distance

The distance in this case is the turning radius of the crank, which is 0.25 m.

The torque needed to counteract the weight of the bucket is therefore:

Torque = Weight of bucket x turning radius = 225.4 N x 0.25 m = 56.35 Nm

The force required can then be found using the torque equation:

Torque = force x distance

Rearranging the equation, we get:

Force = torque / distance = 56.35 Nm / 0.080 m = 704.4 N

Therefore, the minimum force directed perpendicular to the crank handle required to just raise the bucket is 72 N, which is closest to option C.

Question 3

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

Accepted Answer

Angular acceleration can be measured in radians per second squared (rad/s^2) or degrees per second squared (deg/s^2), which is equivalent to rad/s/s or deg/s/s. Therefore, option C is the only one that has rad/s^2 as an option for angular acceleration. Angular velocity can be measured in radians per second (rad/s), revolutions per minute (rev/min), or degrees per hour (deg/hr), which is equivalent to rad/s or deg/s. Option C also has deg/hr as an option for angular velocity, making it the best choice.

Question 4

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.

Accepted Answer

Torque is calculated as the product of force and the perpendicular distance from the axis of rotation. Here, Torque = 300 N * 1.2 m = 360 N·m.

Question 5

A grindstone spinning at the rate of 12 rev/s has what approximate angular speed?

Accepted Answer

The answer of A grindstone spinning at the rate of...

Question 6

Calculate the linear speed due to the Earth's rotation for a person at a point on its surface located at 30^o N latitude.The radius of the Earth is 6.40 × 10⁶ m.

Accepted Answer

The answer of Calculate the linear speed due to the...

Question 7

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)

Accepted Answer

The torque produced by the weight of the bucket and water is given by the formula: torque = force x lever arm. The force is equal to the weight of the bucket and water, which is 23 kg x 9.8 m/s^2 = 225.4 N. The lever arm is the radius of the cylinder, which is 0.080 m. Therefore, torque = 225.4 N x 0.080 m = 18 N·m. The correct choice is B.

Question 8

A uniform meterstick balances on a fulcrum placed at the 40-cm mark when a weight W is placed at the 20-cm mark.What is the weight of the meterstick?

Accepted Answer

The meterstick balances at the 40-cm mark, meaning the torques on either side are equal. The weight W creates a torque of W * 20 cm. For the meterstick to balance, its weight must create an equal torque on the other side. Since the center of mass of the uniform meterstick is at the 50-cm mark, the torque due to the meterstick's weight is its weight times 10 cm. Therefore, the weight of the meterstick is 2W.

Question 9

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. )

Accepted Answer

The answer of Two children seat themselves on a seesaw.The...

Question 10

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?

Accepted Answer

The average angular acceleration can be calculated using the formula: (final angular velocity - initial angular velocity) / time. Here, it is (11.0 rad/s - 2.0 rad/s) / 2.1 s = 4.3 rad/s².

Question 11

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.

Accepted Answer

The ratio of the distance from the center to point 1 and the distance from point 1 to point 2 is given by (11ea7a51_6362_2f53_89bd_3f32ce3ea797_TB5259_11)/(11ea7a51_6362_2f52_89bd_231f3173e0f0_TB5259_11). This ratio is the largest because both the numerator and denominator are positive and the numerator is increasing at a greater rate than the denominator, due to the increasing angular velocity.

Question 12

Tasha has mass 20 kg and wants to use a 6.0-m board of mass 10 kg as a seesaw.Her friends are busy,so Tasha seesaws by herself by putting the support at the system's center of gravity when she sits on one end of the board.How far is she from the support point?

Accepted Answer

The answer of Tasha has mass 20 kg and wants...

Question 13

A ceiling fan is turned on and reaches an angular speed of 120 rev/min in 20 s.It is then turned off and coasts to a stop in an additional 60 s.The ratio of the average angular acceleration for the first 20 s to that for the last 60 s is which of the following?

Accepted Answer

Using the formula:
ω = ω0 + αt

Where:
ω0 = initial angular velocity
ω = final angular velocity
α = angular acceleration
t = time

For the first part, we have:
ω0 = 0 (initially not moving)
ω = 120 rev/min
t = 20 s

So, α1 = (ω - ω0)/t = 6 rev/min^2

For the second part, we have:
ω0 = 120 rev/min (initially moving)
ω = 0 (coasting to a stop)
t = 60 s

So, α2 = (ω - ω0)/t = -2 rev/min^2

The ratio of average angular accelerations is:
α1/α2 = (6 rev/min^2)/(-2 rev/min^2) = -3

Therefore, the answer is B) -3.

Question 14

A 3.0-m rod is pivoted about its left end.A force of 10 N is applied perpendicular to the rod at a distance of 1.2 m from the pivot causing a ccw torque,and a force of 5.2 N is applied at the end of the rod 3.0 m from the pivot.The 5.2-N force is at an angle of 30^o to the rod and causes a cw torque.What is the net torque about the pivot? (Take ccw as positive. )

Accepted Answer

The torque from the 10 N force is 10 N * 1.2 m = 12 N·m (ccw, positive). The torque from the 5.2 N force is 5.2 N * 3.0 m * sin(30°) = 7.8 N·m (cw, negative). The net torque is 12 N·m - 7.8 N·m = 4.2 N·m.

Question 15

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?

Accepted Answer

At the bottom of the circle, the tension in the string is given by:$$T = mg + mv^2/r$$where:* m is the mass of the object* g is the acceleration due to gravity* v is the speed of the object* r is the radius of the circlePlugging in the given values, we get:$$T = (0.200 kg)(9.81 m/s^2) + (0.200 kg)(8.00 rad/s)^2(0.500 m)$$$$T = 8.36 N$$Therefore, the correct answer is A.

Question 16

A uniform bridge span weighs 70.0 × 10³ N and is 40.0 m long.An automobile weighing 15.0 × 10³ N is parked with its center of gravity located 12.0 m from the right pier.What upward support force does the right pier provide?

Accepted Answer

The total torque about the left pier must be zero for equilibrium. The torque due to the bridge's weight acts at its center (20 m from the left pier), and the torque due to the car acts 28 m from the left pier. Solving for the right pier's force gives 45.5 × 10³ N.

Question 17

A 0.60-kg rock is swung in a circular path and in a vertical plane on a 0.25-m length string.At the top of the path,the angular speed is 12.0 rad/s.What is the tension in the string at that point?

Accepted Answer

The tension in the string at the top of the path is calculated using the formula T = m(v^2/r) - mg, where v = ωr. Substituting the given values, T = 0.60*(12*0.25)^2/0.25 - 0.60*9.8 = 16 N.

Question 18

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.

Accepted Answer

The formula for the length of thread on a spool is:

length = (2πr) * turns

Where r is the radius of the spool and turns is the number of turns of thread on the spool.

To find the number of turns, we rearrange this formula:

turns = length / (2πr)

We are given that the length is 126 m and the average radius is 1.00 cm, which is 0.01 m.

turns = 126 / (2π(0.01)) = 2000

Therefore, the number of turns of thread on the spool is 2000. Answer choice C is correct.

Question 19

1300 rev/min is equivalent to which of the following?

Accepted Answer

To convert from rev/min to rad/s, we need to remember that there are 2π radians in one revolution, and 60 seconds in one minute. So, we can use the conversion factor:

1300 rev/min x 2π radians/1 rev x 1 min/60 s = 136 rad/s

Therefore, the answer is B).

Question 20

Suppose a car has a 100,000 mile 10 year warranty on the wheels and axles of a car.How may turns will the wheels of 0.80-m diameter make if both the mileage and time warranties run out simultaneously and what will be the average angular velocities of the wheel? (Assume that a mile = 1.6 x 10³ M and that a year is 3.16 x 10⁷ S)

Accepted Answer

The number of turns is calculated by dividing the total distance by the circumference of the wheel. The average angular velocity is found by dividing the total angular displacement by the total time.

Quiz 8: Rotational Equilibrium and Rotational Dynamics: Part A

The torque caused by a force F applied at a distance r from the axis of rotation,is given by τ = rFsinθ,where θ is the angle between And ) If the magnitudes r and F remain the same,what other angle θ' will produce the same torque as was produced at angle θ if θ was less than 90°?

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

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 grindstone spinning at the rate of 12 rev/s has what approximate angular speed?

Calculate the linear speed due to the Earth's rotation for a person at a point on its surface located at 30^o N latitude.The radius of the Earth is 6.40 × 10⁶ m.

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 uniform meterstick balances on a fulcrum placed at the 40-cm mark when a weight W is placed at the 20-cm mark.What is the weight of the meterstick?

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?

Tasha has mass 20 kg and wants to use a 6.0-m board of mass 10 kg as a seesaw.Her friends are busy,so Tasha seesaws by herself by putting the support at the system's center of gravity when she sits on one end of the board.How far is she from the support point?

A ceiling fan is turned on and reaches an angular speed of 120 rev/min in 20 s.It is then turned off and coasts to a stop in an additional 60 s.The ratio of the average angular acceleration for the first 20 s to that for the last 60 s is which of the following?

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 uniform bridge span weighs 70.0 × 10³ N and is 40.0 m long.An automobile weighing 15.0 × 10³ N is parked with its center of gravity located 12.0 m from the right pier.What upward support force does the right pier provide?

A 0.60-kg rock is swung in a circular path and in a vertical plane on a 0.25-m length string.At the top of the path,the angular speed is 12.0 rad/s.What is the tension in the string at that point?

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.

1300 rev/min is equivalent to which of the following?

Quiz 8: Rotational Equilibrium and Rotational Dynamics: Part A

The torque caused by a force F applied at a distance r from the axis of rotation,is given by τ = rF​sinθ,where θ is the angle between And ) If the magnitudes r and F remain the same,what other angle θ' will produce the same torque as was produced at angle θ if θ was less than 90°?

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

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 grindstone spinning at the rate of 12 rev/s has what approximate angular speed?

Calculate the linear speed due to the Earth's rotation for a person at a point on its surface located at 30o N latitude.The radius of the Earth is 6.40 × 106 m.

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 uniform meterstick balances on a fulcrum placed at the 40-cm mark when a weight W is placed at the 20-cm mark.What is the weight of the meterstick?

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?

Tasha has mass 20 kg and wants to use a 6.0-m board of mass 10 kg as a seesaw.Her friends are busy,so Tasha seesaws by herself by putting the support at the system's center of gravity when she sits on one end of the board.How far is she from the support point?

A ceiling fan is turned on and reaches an angular speed of 120 rev/min in 20 s.It is then turned off and coasts to a stop in an additional 60 s.The ratio of the average angular acceleration for the first 20 s to that for the last 60 s is which of the following?

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 uniform bridge span weighs 70.0 × 103 N and is 40.0 m long.An automobile weighing 15.0 × 103 N is parked with its center of gravity located 12.0 m from the right pier.What upward support force does the right pier provide?

A 0.60-kg rock is swung in a circular path and in a vertical plane on a 0.25-m length string.At the top of the path,the angular speed is 12.0 rad/s.What is the tension in the string at that point?

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.

1300 rev/min is equivalent to which of the following?

The torque caused by a force F applied at a distance r from the axis of rotation,is given by τ = rFsinθ,where θ is the angle between And ) If the magnitudes r and F remain the same,what other angle θ' will produce the same torque as was produced at angle θ if θ was less than 90°?

Calculate the linear speed due to the Earth's rotation for a person at a point on its surface located at 30^o N latitude.The radius of the Earth is 6.40 × 10⁶ m.

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 uniform bridge span weighs 70.0 × 10³ N and is 40.0 m long.An automobile weighing 15.0 × 10³ N is parked with its center of gravity located 12.0 m from the right pier.What upward support force does the right pier provide?