Torque

What is the net torque on the bar shown in (Figure 1), about the axis indicated by the dot? Suppose that F = 17 N .

F*Distance from pivot point 17*.75 12.75

True or false: The quantity represented by θ0theta_0 is a function of time (i.e., is not constant).

False

True or false: The quantity represented by ω0 is a function of time (i.e., is not constant).

False

force 2F→2 acts half as far from the pivot as 1F→1. What magnitude of 2F→2 causes the net torque on the rod to be zero?

In order for the NET torque = 0, the CW torque must equal the CCW torque: F2 • d = F1(sin 45°) • 2d F2 = (20.0)(sin 45°) • 2 = 40.0(sin 45°) ≈ 28.3 N ANS

A turntable is rotating at 33 1/3 rpm. You then flip a switch, and the turntable speeds up, with constant angular acceleration, until it reaches 78 rpm

More information is needed before t can be found.

In the equation ω=ω0+αtω=ω0+αt, what does the time variable t represent? (always true)

the time elapsed from when the angular velocity equals ω0 until the angular velocity equals ω.

Dario, a prep cook at an Italian restaurant, spins a salad spinner and observes that it rotates 20.0 times in 5.00 seconds and then stops spinning it. The salad spinner rotates 6.00 more times before it comes to rest. Assume that the spinner slows down with constant angular acceleration. What is the magnitude of the angular acceleration of the salad spinner as it slows down?

α=8.38 radians/s2

Suppose you are asked to find the amount of time t, in seconds, it takes for the turntable to reach its final rotational speed. Which of the following equations could you use to directly solve for the numerical value of t?

More information is needed before t can be found. Knowing ωomega and ω0omega_0 would not be enough information to allow you to solve for t; you would need additional information (namely, the value of the angular acceleration αalpha) before you could find a numerical value for t.

If Luis pulls straight down on the end of a wrench that is tilted θ = 30∘ above the horizontal and is r = 29 cm long, what force must he apply to exert a torque of -21 N⋅m ?

T= F*r*cosθ -21=F(.29)[cos(30)] F= 84N

You are now given an additional piece of information: It takes five complete revolutions for the turntable to speed up from 33 1/3 rpm to 45 rpm. Which of the following equations could you use to directly solve for the numerical value of the angular acceleration α?

ω2=ω^2o+2α(θ−θ0)

The mass of block B is twice the mass of block A, while the mass of the pulley is equal to the mass of block A. The blocks are let free to move and the cord moves on the pulley without slipping or stretching. There is no friction in the pulley axle, and the cord's weight can be ignored. -Which of the following statements correctly describes the system shown in the figure?

The angular acceleration of the pulley is nonzero.

The mass of block B is twice the mass of block A, while the mass of the pulley is equal to the mass of block A. The blocks are let free to move and the cord moves on the pulley without slipping or stretching. There is no friction in the pulley axle, and the cord's weight can be ignored. -What happens when block B moves downward?

The cord's tension on the right side of the pulley is higher than on the left side.

True or false: The quantity represented by θθtheta is a function of time (i.e., is not constant).

True

True or false: The quantity represented by ω is a function of time (i.e., is not constant).

True

In the equation ω=ωi+αt, what does the time variable t represent?

the time elapsed from when the angular velocity equals ω0ω0 until the angular velocity equals ω

Which of the following equations is not an explicit function of time t, that is, does not involve t as a variable, and is therefore useful when you do not know or do not need the time?

ω^2=ω^20+2α(θ−θ0)