A torque of 50.0 N-m is applied to a grinding wheel (I = 20.0 kg-m²) for 20 s. (a) If it starts from rest, what is the angular velocity of the grinding wheel after the torque is removed? (b) Through what angle does the wheel move through while the torque is applied?

A constant torque acts on a merry-go-round. The power input of the torque is $(a)$ constant, $(b)$ proportional to the angular speed of the merry-go-round, $(c)$ zero, $(d)$ none of these.

The dividends (in dollars) per share declared by Coca-Cola for the years 1995 through 2010 are shown in the table.

$$\begin{matrix} \text{Year } & \text{Dividend, D}\\ \text{1995} & \text{0.44}\\ \text{1996} & \text{0.50}\\ \text{1997} & \text{0.56}\\ \text{1998} & \text{0.60}\\ \text{1999} & \text{0.64}\\ \text{2000} & \text{0.68}\\ \text{2001} & \text{0.72}\\ \text{2002} & \text{0.80}\\ \text{2003} & \text{0.88}\\ \text{2004} & \text{1.00}\\ \text{2005} & \text{1.12}\\ \text{2006} & \text{1.24}\\ \text{2007} & \text{1.36}\\ \text{2008} & \text{1.52}\\ \text{2009} & \text{1.64}\\ \text{2010} & \text{1.76}\\ \end{matrix}$$

 (a) Use a graphing utility to create a scatter plot of the data. Let represent the year, with corresponding to 1995. (b) Use the regression feature of the graphing utility to find a linear model and a quadratic model for the data. (c) Use the graphing utility to graph each model from part (b) with the data. (d) Which model do you think better fits the data? Explain your reasoning. (e) Use the model you selected in part (d) to predict the dividends per share in 2011 and 2015. Coca-Cola predicts the dividends per share to be about $1.88 in 2011 and to reach$2.48 by one of the years from 2013 to 2015. Do your predictions support those of Coca-Cola? Explain.

Estimate the net torque about the axle of the wheel shown in given Figure. Assume that a friction torque of $0.40 \mathrm{~m} \cdot \mathrm{~N}$ opposes the motion.

Describe the operation(s) for the expression. $\frac{z-y}{x}$

Figure shows an apparatus used to measure the speed distribution of gas molecules. It consists of two slotted rotating disks separated by a distance $d$, with the slots displaced by the angle $\theta$. Suppose the speed of light is measured by sending a light beam from the left through this apparatus. (a) Show that a light beam will be seen in the detector (that is, will make it through both slots) only if its speed is given by $c=\omega d / \theta$, where $\omega$ is the angular

A 20-turn $5.0 \mathrm{cm}$ by $5.0 \mathrm{cm}$ coil hangs with the plane of the coil parallel to a $0.12-\mathrm{T}$ magnetic field. (a) Determine the torque on the coil when there is a $0.50-\mathrm{A}$ current through it.(b) The support for the coil exerts an opposing torque, which increases as the coil is deflected. The opposing torque is calculated using the equation $\tau=-0.016 \theta$ (in units of $\mathrm{N} \cdot \mathrm{m}$ ), with the angle $\theta$ in units of radians. At approximately what angle does the magnetic torque balance the torque caused by the supporting wire?

Identify each of the following claims as true or incorrect. Any unbalanced mass can be replaced by two equivalent unbalanced masses in the end planes of the rotor.

If a single force acts on an object and the torque caused by the force is nonzero about some point, is there any other point about which the torque is zero?

Liz decides to save money to buy an electric car. She invests $500 every 6 months at 6.8%/a compounded semi-annually. What total amount of money will she have at the end of the 10th year?

The helicopter is stationary. The $z$ axis of the body-fixed coordinate system points downward and is coincident with the axis of the helicopter's rotor. The moment of inertia of the rotor about the $z$ axis is $8600 \mathrm{~kg}-\mathrm{m}^2$. Its angular velocity is $-258 \mathrm{k}(\mathrm{rpm})$. If the helicopter begins a pitch maneuver during which its angular velocity is $0.02 \mathrm{~J}(\mathrm{rad} / \mathrm{s})$, what is the magnitude of the gyroscopic moment exerted on the helicopter by the rotor? Does the moment tend to cause the helicopter to roll about the $x$ axis in the clockwise direction (as seen in the photograph) or the counterclockwise direction?

Reread lines 128-141. How did Abuelita get locked in the shed this time? Cite text evidence in your response.

The gyro rotor is spinning at the constant rate of 100 rev/min relative to the x-y-z axes in the direction. If the angle $\gamma$ between the gimbal ring and the horizontal X-Y plane is made to increase at the constant rate of 4 rad/s and if the unit is forced to precess about the vertical at the constant rate N = 20 rev/min, calculate the magnitude of the angular acceleration $\alpha$ of the rotor when $\gamma$ = 30$^\circ$. Solve by using $\left(\frac{d \mathbf{V}}{d t}\right)_{X Y Z}=\left(\frac{d \mathbf{V}}{d t}\right)_{x y z}+\mathbf{\Omega} \times \mathbf{V}$ applied to the angular velocity of the rotor.

For the steel shaft shown in given figure, (a) Find the maximum torque transmitted by any transverse cross section of the shaft. (b) Draw a torque diagram for the shaft.