A circular-motion addict of mass 80 kg rides a Ferris wheel around in a vertical circle of radius 12 m at a constant speed of 5.5 m/s. (a) What is the period of the motion? What is the magnitude of the normal force on the addict from the seat when both go through (b) the highest point of the circular path and (c) the lowest point?

The slotted arm $O A$ rotates counterclockwise about $O$ with a constant angular velocity of $\dot{\theta}$. The motion of pin $B$ is constrained such that it moves on the fixed circular surface and along the slot in $O A$. Determine the magnitudes of the velocity and acceleration of pin $B$ as a function of $\theta$. The distance $OB =r = 2a\cos\theta$. Where $a$ is the radius of circular surface.

Railroad tracks follow a circular curve of radius 500.0 m and are banked at an angle of 5.00°. For trains of what speed are these tracks designed?

An electric field of magnitude $200.0 \mathrm{~V} / \mathrm{m}$ is directed perpendicular to a circular planar surface with radius $6.00 \mathrm{~cm}$. If the electric field increases at a rate of $10.0 \mathrm{~V} /(\mathrm{m} \mathrm{s})$, estimate the magnitude and the direction of the magnetic field at a radial distance $10.0 \mathrm{~cm}$ away from the center of the circular area.

Is the following statement correct? If not rewrite it so that it is correct. The superscript zero in $\Delta H_f^{\circ}$ means that the reactions conditions are $298.15 \mathrm{~K}$.

What is the circular velocity of an Earth satellite 1000 km above Earth's surface? (Hint: Earth's radius is 6380 km.)

Complete and balance the equation for gas-evolution reactions.

(NH$_4)_2$SO$_4$(aq)+Ca(OH)$_2$(aq) $\rightarrow$

Use Lagrange multipliers to find the dimensions of a right circular cylinder with volume V_0 cubic units and minimum surface area.

The area A of a circle with diameter d is given by $A = \pi \left( \frac { d } { 2 } \right) ^ { 2 }$ Use this relationship to a. verify that doubling the length of the diameter of a circular skating rink increases the area of the rink by a factor of $2 ^ { 2 }$. b. verify that tripling the length of the diameter of a circular skating rink increases the area of the rink by a factor of $3 ^ { 2 } .$

A stuntman whose mass is 70 kg swings from the end of a 4.0-m-long rope along the arc of a vertical circle. Assuming he starts from rest when the rope is horizontal, find the tensions in the rope that are required to make him follow his circular path at a height of 1.5 m above the bottom of the circular arc.

Use the figure and any appropriate relationship(s) among circular functions to find the value.

$$\cos \frac{7 \pi}{6}$$

The maximum allowable value of each of the reactions is $180 \mathrm{~N}$. Neglecting the weight of the beam, determine the range of the distance $d$ for which the beam is safe.

What is the approximate area of a circular pond that has a radius of 35 meters? Tell what value you used for $\pi.$

From Newton to Dark Matter. Show that the equation $M= r\times v^{2}/G$ from is equivalent to Newton’s version of Kepler’s third law. Assume that one mass is much larger than the other mass and that the orbit is circular. (Hint: What is the mathematical relationship between period p and orbital velocity v and orbital radius r for a circular orbit?)