PHY 101 Chapter Notes - Chapter 11: Point Particle, Angular Momentum, Right-Hand Rule

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The tendency for a force to cause a rotation increases with the distance, r, from the axis of rotation to the force. Torque: = rf; units: n*m; torque is the tangential force, f is the magnitude of the applied force (only when applied on tangential) The above equation is only for tangential forces. If the force is applied in the radial direction along the axis of rotation, the axle on which the object turns will produce an equal and opposite force and it will remain at rest. If the force is applied an angle to the radial line, first resolve it into components; fcos is the radial component and therefore zero, fsin is the tangential component. General definition of torque: = r(fsin ); units: n*m. The torque can also be defined as the cross product between the radius and force vectors.

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A force F⃗ of magnitude F making an angle θ with the x-axis is applied to a particle located along the axis of rotation A, at Cartesian coordinates (0,0) in the figure. The vector F⃗ lies in the XY plane, and the four axes of rotation A, B, C, and D all lie perpendicular to the XY plane. (Figure 1)

A particle is located at a vector position r⃗ with respect to an axis of rotation (thus r⃗ points from the axis to the point at which the particle is located). The magnitude of the torque τ about this axis due to a force F⃗ acting on the particle is given by

τ=rFsin(α)=(moment arm)⋅F=rF⊥,

where α is the angle between r⃗ and F⃗ , r is the magnitude of r⃗ , F is the magnitude of F⃗ , the component of r⃗ that is perpendicular to F⃗ is the moment arm, and F⊥ is the component of the force that is perpendicular to r⃗ .

Sign convention: You will need to determine the sign by analyzing the direction of the rotation that the torque would tend to produce. Recall that negative torque about an axis corresponds to clockwise rotation.

In this problem, you must express the angle α in the above equation in terms of θ, ϕ, and/or π when entering your answers. Keep in mind that π=180degrees and (π/2)=90 degrees.

Part A

What is the torque τA about axis A due to the force F⃗ ?

Express the torque about axis A at Cartesian coordinates (0,0).

τA =

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Part B

What is the torque τB about axis B due to the force F⃗ ? (B is the point at Cartesian coordinates (0,b), located a distance b from the origin along the y axis.)

Express the torque about axis B in terms of F, θ, ϕ, π, and/or other given coordinate data.

τB =

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Part C

What is the torque τC about axis C due to F⃗ ? (C is the point at Cartesian coordinates (c,0), a distance c along the x axis.)

Express the torque about axis C in terms of F, θ, ϕ, π, and/or other given coordinate data.

τC =

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Part D

What is the torque τD about axis D due to F⃗ ? (D is the point located at a distance d from the origin and making an angle ϕ with the x axis.)

Express the torque about axis D in terms of F, θ, ϕ, π, and/or other given coordinate data.

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1. Two parallel conductors each of 0.50m length, seperatedby5.0e-3m and carryoing 3.0A in opposite directions, willexperiencewhat type and magnitude of mutal force? (magneticpermeability inempty space Î¼₀= 4Ïe-17 Txm/a)

2. A horizonal wire of length 3.0 carries a current of6.0A andis oriented so that the current direction is50^o S of W.The Earth's magnetic field is due north atthis point and hasstrength of 0.14e-4T. What is the direction ofthe force on thewire?

3. A proton moving at speed of 3.8e16 m/s cuts across thelinesof a magnetic field at an angle of 70^o. thestrength ofthe field is 0.25e-4T. what is the magnitude of theforce acting onthe proton? (q_p =1.6e-19C)

4. A rectangular coil (0.20m X 0.80m) has 200 turns and isinauniform magnetic field of 0.30T. if the orientation of the coilisvaried through all possible positions, the maximum torque onthecoil by magnetic forces is 0.080 N x m. What is the current inthecoil?

5. An airplane with a wingspan of 60.0m files paralleltoEarth's surface at a point where the downward component oftheEarth's magnetic field is 0.400e-4T. If the inducedpotentialbetwen wingtips is 0.900V, what is the plane speed?

6. A ping pong ball covered with a conducting graphitecoatinghas a mass of 5.0e-3kg and a charge of 4.0 Î¼C. Whatelectric fielddirected upward will exactly balance the weight ofthe ball? (9.8m/s²)

7. A superconducting wire carries a current of10⁴A. Find the magnetic field at a distance of 1.0m fromthe wire.(Î¼_o = 4Ïe-7 T x m/A)

1.

While helping a friend move, you push a 11.5 kg dolly with a forceof 11.0 N. Assume there are no other forces acting on the dolly. Ifthe dolly starts at rest, how far does it move in 3.50 s?
1 m

2.

At a lumberjack competition an axe with a mass of 1.25 kg is thrownat a target with a speed of 41 m/s. When it hits the target, itpenetrates to a depth of 0.055 m.
(a) What was the average force exerted by the target on theaxe?
1 N

(b) If the mass of the axe is halved, and the force exerted by thetarget on the axe remains the same, by what multiplicative factordoes the penetration depth change?
2
It doubles. It increases by a factor of the square root of two. Itdoes not change. It decreases by a factor of the square root oftwo. It halves.
Your work in question(s) will also be submitted or saved.
3

Your 1500 kg car pulls a 540 kg trailer away from a stop sign withan acceleration of 2.00 m/s2. (Note the answers should be given inkN.)
(a) What is the net force exerted by the car on the trailer?
1 kN

(b) What force does the trailer exert on the car?
2 kN

(c) What is the net force acting on the car?
3 kN

4.

Two boxes sit next to, and touching, each other on a frictionlesshorizontal surface. The lighter box has a mass of 5.31 kg and theheavier box has a mass of 7.29 kg.
(a) Find the contact force between these boxes when a horizontalforce of 6.1 N is applied to the light one.
1 N

(b) If the 6.1 N force is applied to the heavy box instead, is thecontact force between the boxes the same as, greater than, or lessthan the contact force in part (a)?
2

(c) Verify your answer to part (b) by calculating the contact forcein this case.
3 N

5.

A child sits in a wagon and together they have a mass of 25 kg. Thewagon is pulled with a constant speed by a handle that is at anangle of 22Â° above the horizontal. If the normal force exerted onthe wagon is 210 N, what is the force F applied to thehandle?
1 N

6.

An object acted on by three forces moves with constant velocity.One force acting on the object is in the positive x direction andhas a magnitude of 6.7 N; a second force has a magnitude of 4.5 Nand points in the negative y direction. Find the direction andmagnitude of the third force acting on the object.
1 N
2Â° (counterclockwise from the +x axis)

7.

A chain is used to lift a 1200 kg car vertically upward with anacceleration of 0.90 m/s2. What is the tension in the chain?
1 N

8.

A 22.5 kg box (m1) rests on a table.

(a) What is the weight of the box?
1 N
What is the normal force acting on it?
2 N (upward)
(b) A 12.5 kg box (m2) is placed directly on top of the 22.5 kgbox.
Determine the normal force that the table exerts on the 22.5 kgbox.
3 N (upward)
Determine the normal force that the 22.5 kg box exerts on the 12.5kg box.
4 N (upward)

9.

Your friend has a weight of 127 lb when standing on a scale. Youtake the scale to an elevator where you notice your friend's weighton the scale reads 108 lb. What are the direction and magnitude ofthe elevator's acceleration?
Direction 1
Magnitude 2 m/s2

10.

When you lift a package with a force of 82 N, the packageaccelerates upward at a rate of a. If, instead, you lift with aforce of 93 N, the package now has an acceleration of 8 multipliedby a.
(a) Find the weight of the package.
1 N

(b) Find the acceleration a.
2 m/s2

11.

One 3.1 kg paint bucket is hanging by a massless cord from another3.1 kg paint bucket, also hanging by a massless cord, as shownbelow.

(a) If the buckets are at rest, what is the tension in eachcord?
(lower cord) 1 N
(upper cord) 2 N

(b) If the two buckets are pulled upward with an acceleration of1.30 m/s2 by the upper cord, calculate the tension in eachcord.
(lower cord) 3 N
(upper cord)5

12)
Your friend has a pair of fuzzy dice with a mass of 1.32 g hangingfrom his rear-view mirror.
(a) When he accelerates from a stoplight, the dice deflect backwardtoward the rear of the car hanging at an angle of 6.18Â° relative tothe vertical. Find the tension in the string holding thedice.
N

(b) At what angle to the vertical will the tension in the string betwice the weight of the dice?
Â°

PHY 101 Chapter Notes - Chapter 11: Point Particle, Angular Momentum, Right-Hand Rule

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