Kinesiology 2241A/B Lecture Notes - Lecture 20: Right-Hand Rule, Angular Velocity, Angular Acceleration

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copperlizard489

14 Mar 2018

School

Western University

Department

Kinesiology

Course

Kinesiology 2241A/B

Professor

Thomas Richard Jenkyn

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Document Summary

Just like linear speed and velocity, angular speed and velocity are not the same thing. Angular velocity is a vector with al 4 attributes of a vector: Direction is the axis of rotation following the right-hand rule. Point of application is the center of rotation (and not the center of mass! Line of action runs along the axis of rotation. Angular velocity is the rate at which the angle change with respect to time. Right hand rule for an angular velocity vector. Final exam question, will have an athlete in the air with axis posted and we"ll need to figure out the axis of rotation based on this rule. Angular velocity is the vector w that points along the axis of rotation according to the right-hand rule. The length of w is the angular speed. Linear velocity is the vector v that points along the tangent to the pathway (black line) and at a right angle tot the radius r.

Related Questions

Two masses (M and M) are attachedto the ends of a massless rigid rod. The rod is mounted on an axle(the axis of rotation is the z axis) through the center; the twomasses are both at distance R from the axle. The masses and rod areinitially at rest.
A third mass m, with initial velocity v0 [^(j)], will collide headon with the mass M on the right, as shown. The collision isperfectly elastic. After the collision the mass m will eithercontinue moving in the same direction or it will bounce back andmove in the -y direction.

(A) Determine the final speed of m.
(B) Find the condition on the masses such that the mass m bouncesbackward.
(C) Determine the final angular velocity of the rod.
[[Hint: What quantities are constants of the motion?]]

x.Hm

I just need help in the three questionI figure the last question

1)Consider an oxygen molecule (O2) rotating inthe xy plane about the z axis. The axis

passes through the center of the molecule,perpendicular to its length. The mass of each

oxygen atom is 2.66 x 10

-26 kg, and at room temperature the average separation between

the two atoms is

d=1.21 x 10-10 m (the atoms are treated as point masses).a) Calculate

the moment of inertia of the molecule about the zaxis. b) If the angular speed of the

molecule about the

z axis 4.60 x 1012 rad/s, what is its rotational kineticenergy?

Answer: a) 1.95 x 10

-46 kg.m2 b) 2.06 x 10-21 J

2) A wheel rotates with a constant angularacceleration of 3.50 rad/s2. If the angular speed

of the wheel is 2.00 rad/s at

ti = 0, a) through what angle does the wheel rotate in2.00 s?

Answer a) 6300

3)A uniform rod of length L and mass M is free to rotate on africtionless pin passing

through one end as shown in question 4 below. Therod is released from rest in the

horizontal position. a) What is its angular speedwhen it reaches its lowest position?

b) Determine the linear speed of the center ofmass and the linear speed of the lowest

point on the rod when it is in the verticalposition.

Answer: a)

3g b) Center of mass speed =3gL

1 ;

Linear speed of the lowest point =3gL

(Hint, use mechanical energy conservation)

4 A uniform rod of length L and mass M is attached at one endto a frictionless pivot and is

free to rotate about the pivot in the verticalplane, as shown in Figure below. The rod is

released from rest in the horizontal position. a)What is the initial angular acceleration of

the rod and b) the initial linear acceleration ofits right end? Answer: a)

Answer: a)

g b) Center of mass speed = 3gL

1 ;

Linear speed of the lowest point =3

(Hint, use mechanical energyconservation)

I would appreciate help with any of the following problems. Thankyou.

22. In an isometric exercise a person places a hand on a scale andpushes vertically downward, keeping the forearm horizontal. This ispossible because the triceps muscle applies an upward forceperpendicular to the arm, as the figure indicates. The forearmweighs 22.1 N and has a center of gravity as indicated. The scaleregisters 113 N. Determine the magnitude of .
Distance between the force applied by the muscle and the elbowjoint 0.025 m. The distance between the elbow joint and the armscenter of gravity is 0.15 m. Distance between the arms center ofgravity and the center of the scale is 0.15 m. I was not able tofind the answer to this problem using the solution posted on thewebsite.

26.A wrecking ball (weight = 4310 N) is supported by a boom, whichmay be assumed to be uniform and has a weight of 2550 N. As thedrawing shows, a support cable runs from the top of the boom to thetractor. The angle between the support cable and the horizontal is32Â°, and the angle between the boom and the horizontal is 48Â°. Find(a) the tension in the support cable and (b) the magnitude of theforce exerted on the lower end of the boom by the hinge at pointP.

56. Two identical wheels are moving on horizontal surfaces. Thecenter of mass of each has the same linear speed. However, onewheel is rolling, while the other is sliding on a frictionlesssurface without rolling. Each wheel then encounters an inclineplane. One continues to roll up the incline, while the othercontinues to slide up. Eventually they come to a momentary halt,because the gravitational force slows them down. Each wheel is adisk of mass 3.64 kg. On the horizontal surfaces the center of massof each wheel moves with a linear speed of 5.26 m/s. (a),(b) Whatis the total kinetic energy of each wheel? (c), (d) Determine themaximum height reached by each wheel as it moves up the incline. Iwas able to solve for the rolling wheel but couldn't find the rightanswers for the sliding wheel.

66. A thin uniform rod is rotating at an angular velocity of 1.89rad/s about an axis that is perpendicular to the rod at its center.As the figure indicates, the rod is hinged at two places,one-quarter of the length from each end. Without the aid ofexternal torques, the rod suddenly assumes a "u" shape, with thearms of the "u" parallel to the rotation axis. What is the angularvelocity of the rotating "u"?

76. A woman who weighs 501 N is leaning against a smooth verticalwall, as the drawing shows. Find (a) the magnitude of the force N(directed perpendicular to the wall) exerted on her shoulders bythe wall and the (b) horizontal and (c) vertical components of theforce exerted on her shoes by the ground.

Kinesiology 2241A/B Lecture Notes - Lecture 20: Right-Hand Rule, Angular Velocity, Angular Acceleration

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