PHYS 100 Chapter Notes - Chapter 9: Angular Velocity, Mechanical Advantage, Free Body Diagram

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ochrebat842

10 May 2018

School

Simon Fraser University

Department

Physics

Course

PHYS 100

Professor

Simon Watkins

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Chapter 9

Statics and Torque

- Torque is defined as force x distance

o Tirque moving in clockwise, negative

o Counterclockwise, positive

o Torque changes angular velocity

o The harder you pull, the more torque is

generated and more change in angular

velocity

o The amount of force affects torque and the

placement of force

o Angle between applied force and radius

▪ τ = r⊥ F

▪ τNet = a(I)

• Angular acceleration (Inertia)

o Moment of Inertia = ∑m(r2)

▪ Mass(Distance of mass from axis of rotation2)

• Further the mass, the higher the objects moment of inertia

o Torque has the ability to do force

- The first condition for Equilibrium

o The first condition necessary to achieve equilibrium is “the net external force for

the system must be zero

▪ Net F = 0

o If Net F is zero, then the external force in any direction is zero

- The second condition for Equilibrium

o Achieve equilibrium involves avoiding accelerated rotation. A rotation body or

system can be in equilibrium if its rate of rotation is constant and remains

unchanged by the forces acting on it

o Torque is the turning or twisting of a force

▪ Torque, has both magnitude and direction

• Counterclockwise torque is produced by this force, the door will

rotate in a counterclockwise due to F

▪ Torque is the rotational equivalent of a force.

• It is a measure of the effectiveness of a force in changing or

accelerating a rotation

o τ = rF Sinθ

▪ τ is the symbol for torque

▪ r is the distance from the pivot point to the point of

force

▪ F is the magnitude of the force

▪ Θ is the angle between the force and the vector

directed from the point of application to the pivot

point

o r⊥ = r sinθ

▪ r⊥ is the name of perpendicular lever arm

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Related Questions

A small piece of cheese is at the center of a disk of radiusRrotating about its axis. A hungry mouse is sitting at the edgeofthe disk. It will be able to eat the cheese when it is a distancer= R/4 from the center of the disk. The surface of thedisk,however, is slippery ...
In the following, assume that the disk is spinning freely aboutitsaxis and that there is no net external torque acting onthesystem.
a) Write expressions for the moment of inertia of the system(diskplus mouse) when the mouse is at the edge (distanceR) andwhen the mouse is at the distance r fromthe center. Themoment of inertia of the disk is I=(1/2)MR².
b) As the mouse approaches the center, does the disk speed up,slowdown, or maintain its angular velocity?
c) Assuming the angular velocity is wwhen the mouse is at the edgeof the disk, find an expression forthe angular velocityw_r whenthe mouse is a distance r = R/4from thecenter.
d) Evaluate the angular velocity w_r for the case thatthe mass of thedisk is M = 18 g, the mass of the mouse ism = 16g, and w = 4 s^-1. Answer:w_r =10 s^-1.
e) Determine if a static friction coefficient of m_s =0.7 is sufficient to prevent themouse from slipping at r =R//4 for R =0.4 m. Please use g = 10m/s².

A bicycle wheel is mounted on a fixed, frictionless axle, with alight string wound around its rim. The wheel has a moment of inertia I = kmr², where m is its mass, r is its radius, and k is a dimensionless constant between zero and one. The wheel is rotating counterclockwise with angular velocity , when at time t someone starts pulling the string with a force of magnitude F. Assume that the string does not slip on the wheel.

What is the instantaneous power

delivered to the wheel via the force

at time $t = 0$

Express the power in terms of some of the variables given in the problem introduction.

maroontortoise635

what is the final angular velocity, ωf, of the two disks? express ωf in terms of it, ir, and ωi.

Consider a turntable to be a circular disk of moment of inertia It rotating at a constant angular velocity ωi(note that angular velocities use the Greek letteromega and not double-u) around an axis through the center and perpendicular to the plane of the disk (the disk's "primary axis of symmetry") as shown in(Figure 1) . The axis of the disk is vertical and the disk is supported by frictionless bearings. The motor of the turntable is off, so there is no external torque being applied to the axis.

Another disk (a record) is dropped onto the first such that it lands coaxially (the axes coincide). The moment of inertia of the record is Ir. The initial angular velocity of the second disk is zero.

There is friction between the two disks.

After this "rotational collision," the disks will eventually rotate with the same angular velocity.

Part A

What is the final angular velocity, ωf, of the two disks?

Express ωf (omega subscript f) in terms of It, Ir, and ωi (omega subscript i).

Part B

Because of friction, rotational kinetic energy is not conserved while the disks' surfaces slip over each other. What is the final rotational kinetic energy, Kf, of the two spinning disks?

Express the final kinetic energy in terms of It, Ir, and the initial kinetic energy Ki of the two-disk system. No angular velocities should appear in your answer.

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PHYS 100 Chapter Notes - Chapter 9: Angular Velocity, Mechanical Advantage, Free Body Diagram

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