Explain why the electron moves at constant speed.

Explain why the electron moves on a circular path.

State the direction of the resultant force on the ball.

Calculate the time for one complete revolution.

An object hangs from a light string and moves in a horizontal circle of radius r.

The string makes an angle θ with the vertical. The angular speed of the object is ω. What is tan θ?

A. $\frac{{\omega }^{2}r}{g}$

B. $\frac{g}{{\omega }^{2}r}$

C. $\frac{\omega r^2}{g}$

D. $\frac{g}{\omega r^2}$

The cable is wound onto a cylinder of diameter 1.2 m. Calculate the angular velocity of the cylinder at the instant when the glider has a speed of 27 m s^–1. Include an appropriate unit for your answer.

A particle of mass 0.02 kg moves in a horizontal circle of diameter 1 m with an angular velocity of 3$\pi$ rad s^-1. 

What is the magnitude and direction of the force responsible for this motion?

Object P moves vertically with simple harmonic motion (shm). Object Q moves in a vertical circle with a uniform speed. P and Q have the same time period T. When P is at the top of its motion, Q is at the bottom of its motion.

What is the interval between successive times when the acceleration of P is equal and opposite to the acceleration of Q?

A. $\frac{T}{4}$

B. $\frac{T}{2}$

C. $\frac{3T}{4}$

D. T

A small ball of weight W is attached to a string and moves in a vertical circle of radius R.

What is the smallest kinetic energy of the ball at position X for the ball to maintain the circular motion with radius R?

A.  $\frac{WR}{2}$

B.  W R

C.  2 W R

D.  $\frac{5WR}{2}$

Explain why the kinetic energy of the proton is constant.

State the direction of the resultant force on the ball.

For this proton, calculate, in s, the time for one full revolution.

A mass m attached to a string of length R moves in a vertical circle with a constant speed. The tension in the string at the top of the circle is T. What is the kinetic energy of the mass at the top of the circle?

A.   $\frac{R\left(T+mg\right)}{2}$

B.   $\frac{R\left(T-mg\right)}{2}$

C.   $\frac{Rmg}{2}$

D.   $\frac{R\left(2T+mg\right)}{2}$

Outline, in terms of the force acting on it, why the Earth remains in a circular orbit around the Sun.

A satellite X of mass m orbits the Earth with a period T. What will be the orbital period of satellite Y of mass 2m occupying the same orbit as X?

A. $\frac{T}{2}$

B. T

C. $\sqrt{2T}$

D. 2T

An object of mass m at the end of a string of length r moves in a vertical circle at a constant angular speed ω.

What is the tension in the string when the object is at the bottom of the circle?

A.     m(ω²r + g)

B.     m(ω²r – g)

C.     mg(ω²r + 1)

D.     mg(ω²r – 1)

The fan is rotating at 120 revolutions every minute. Calculate the centripetal acceleration of the tip of a fan blade.

Mass $M$ is attached to one end of a string. The string is passed through a hollow tube and mass $m$ is attached to the other end. Friction between the tube and string is negligible.

Mass $m$ travels at constant speed $v$ in a horizontal circle of radius $r$. What is mass $M$?

A.  $\frac{m{v}^2}{r}$

B.  $m{v}^{2}rg$

C.  $\frac{mg{v}^2}{r}$

D.  $\frac{m{v}^2}{gr}$

Calculate the value of the centripetal force.

The person must not slide down the wall. Show that the minimum angular velocity $\omega$ of the cylinder for this situation is

$\omega =\sqrt{\frac{g}{\mu R}}$

where $\mu$ is the coefficient of static friction between the person and the cylinder.

An object moves in a circle of constant radius. Values of the centripetal force $F$ are measured for different values of angular velocity $\omega$. A graph is plotted with $\omega$ on the $x$-axis. Which quantity plotted on the $y$-axis will produce a straight-line graph?

A.  $\sqrt{F}$

B.  $F$

C.  $F^2$

D.  $\frac{1}{F}$

Determine the orbital period for the satellite.

Mass of Earth = 6.0 x 10²⁴ kg

The hill at point B has a circular shape with a radius of 20 m. Determine whether the skier will lose contact with the ground at point B.

An object of mass m makes n revolutions per second around a circle of radius r at a constant speed. What is the kinetic energy of the object?

A. 0

B. $\frac{1}{2}{\pi }^{2}m{n}^2{r}^2$

C. $2{\pi }^{2}m{n}^2{r}^2$

D. $4{\pi }^{2}m{n}^2{r}^2$

The player kicks the ball again. It rolls along the ground without sliding with a horizontal velocity of $1.40 {\text{m\hspace{0.05em}s}}^{-1}$. The radius of the ball is $0.11 \text{m}$. Calculate the angular velocity of the ball. State an appropriate SI unit for your answer.

The coefficient of static friction between the person and the cylinder is $0.40$. The radius of the cylinder is $3.5 \mathrm{m}$. The cylinder makes $28$ revolutions per minute. Deduce whether the person will slide down the inner surface of the cylinder.

An object of mass m moves in a horizontal circle of radius r with a constant speed v. What is the rate at which work is done by the centripetal force?

A.     $\frac{m{v}^3}{r}$

B.     $\frac{m{v}^3}{2\pi r}$

C.     $\frac{m{v}^3}{4\pi r}$

D.     zero

Show that the speed v of an electron in the hydrogen atom is related to the radius r of the orbit by the expression

$$v=\sqrt{\frac{k{e}^2}{m_{\text{e}}r}}$$

where k is the Coulomb constant.

Satellite X orbits a planet with orbital radius R. Satellite Y orbits the same planet with orbital radius 2R. Satellites X and Y have the same mass.

What is the ratio $\frac{\text{centripetal acceleration of X}}{\text{centripetal acceleration of Y}}$?

A. $\frac{1}{4}$

B. $\frac{1}{2}$

C. 2

D. 4

Outline why this force does no work on the Moon.

Outline why this force does no work on Phobos.

The radius of the pulley is 2.5 cm. Calculate the angular speed of rotation of the pulley as the load hits the floor. State your answer to an appropriate number of significant figures.