Question 1

Two objects,m₁ and m₂,both of mass m,are placed on a horizontal platform which is rotating at a constant angular velocity.m₁ is located at a distance R from the axis of rotation and m₂ is located at a R.The tangential acceleration of mass m₁ ____ to the tangential acceleration of m₂.

Accepted Answer

The tangential acceleration of an object rotating in a circle is given by a = rω², where r is the distance from the axis of rotation and ω is the angular velocity. Since both objects have the same angular velocity, their tangential accelerations are proportional to their distances from the axis of rotation (a1 = 11a2). Therefore, the tangential acceleration of m₁ is equal to 11 times the tangential acceleration of m₂. Hence, the answer is B, they are equal.

Question 2

The Empire's space station is a long way from any star.It is circular and has a radius of 5.10 km.The angular velocity that is needed to give the station an artificial gravity of 9.80 m/s² at its circumference is

Accepted Answer

The formula for angular velocity (ω) needed to create artificial gravity at a radius (r) is:

ω = √(GM/r^3)

Where G is the gravitational constant and M is the mass of the object (in this case, the space station).

We can rearrange this formula to solve for ω:

ω = √(GM/r^3)

ω = √(9.8 * r)

ω = √(9.8 * 5100)

ω = 70,134.23 m/s

However, this is the velocity needed at the center of the space station. To find the velocity needed at the circumference, we need to divide by the radius:

ω = 70,134.23 / 5100

ω = 13.75 rad/s

Therefore, the closest answer choice is B, 7.0 x 10^-13 rad/s.

Question 3

A wheel rotates with a constant nonzero angular acceleration.Which of the following quantities remains constant in magnitude?

Accepted Answer

C

Question 4

Starting from rest,a disk rotates with constant angular acceleration.If it takes 10 rev to reach an angular velocity $\omega$,then how many additional revolutions are required to reach an angular velocity 2$\omega$?

Accepted Answer

The relationship between angular displacement (θ), angular velocity (ω), and angular acceleration (α) for a rotating object starting from rest is given by ω^2 = 2αθ. When the disk reaches an angular velocity ω, it has made 10 revolutions, which means θ = 10 revs. To double the angular velocity to 2ω, we use the same formula: (2ω)^2 = 4ω^2 = 2αθ'. Solving for θ' gives us θ' = 4θ = 4 * 10 revs = 40 revs in total. Since it already made 10 revolutions to reach ω, it needs an additional 30 revolutions to reach 2ω.

Question 5

The London Eye,which is a giant Ferris wheel,has a diameter of 135 m.It revolves at a constant rate and takes 30 minutes to complete one revolution.What is the linear velocity of a rider in a capsule that is located at the perimeter of the wheel?

Accepted Answer

The linear velocity $v$ of a rider can be calculated using the formula $v = \frac{2\pi r}{T}$, where $r$ is the radius of the wheel and $T$ is the period of one revolution. Given the diameter is 135 m, the radius $r = \frac{135}{2} = 67.5$ m. The period $T = 30$ minutes or $1800$ seconds. Thus, $v = \frac{2\pi(67.5)}{1800} \approx 0.236$ m/s, which rounds to $0.24$ m/s.

Question 6

A point P is at a distance R from the axis of rotation of a rigid body.The linear speed,centripetal acceleration,and tangential acceleration of the point can be expressed as

Accepted Answer

The answer of A point P is at a distance...

Question 7

A wheel rotates through 6.0 rad in 2.0 s as it is uniformly brought to rest.The initial angular velocity of the wheel before braking began was

Accepted Answer

The answer of A wheel rotates through 6.0 rad in...

Question 8

A body that moves with a constant speed in a circle

Accepted Answer

When a body moves in a circle at constant speed, it is undergoing uniform circular motion. Although the speed is constant, the direction of the velocity changes continuously, meaning there is a change in velocity and thus an acceleration towards the center (centripetal acceleration). This acceleration implies a net force acting towards the center (centripetal force). However, since this force acts perpendicular to the direction of motion, no work is done as work is defined as the force component in the direction of motion times the distance moved, and in this case, the angle between force and displacement is 90 degrees, making the work done zero.

Question 9

A record turntable rotates through 5.0 rad in 2.8 s as it is accelerated uniformly from rest.What is the angular velocity at the end of that time?

Accepted Answer

Angular acceleration is given by:$$\alpha = \frac{\omega_f - \omega_i}{t}$$where:* $\alpha$ is the angular acceleration* $\omega_f$ is the final angular velocity* $\omega_i$ is the initial angular velocity* $t$ is the timeIn this problem, we have:* $\omega_i = 0$ (since the turntable starts from rest)* $t = 2.8 \text{ s}$* $\theta = 5.0 \text{ rad}$We can use the following kinematic equation to find $\omega_f$:$$\theta = \omega_i t + \frac{1}{2} \alpha t^2$$Substituting our values into this equation, we get:$$5.0 \text{ rad} = 0 + \frac{1}{2} \alpha (2.8 \text{ s})^2$$Solving for $\alpha$, we get:$$\alpha = \frac{5.0 \text{ rad}}{(2.8 \text{ s})^2} = 0.60 \text{ rad/s}^2$$Now we can use the equation for angular acceleration to find $\omega_f$:$$\omega_f = \omega_i + \alpha t$$Substituting our values into this equation, we get:$$\omega_f = 0 + 0.60 \text{ rad/s}^2 (2.8 \text{ s}) = 1.68 \text{ rad/s}$$Therefore, the angular velocity at the end of that time is 1.68 rad/s, which is closest to choice D) 3.6 rad/s.

Question 10

Two points,A and B,are on a disk that rotates about an axis.Point A is three times as far from the axis as point B.If the speed of point B is v,then what is the speed of point A?

Accepted Answer

The speed of a point on a rotating disk can be found using the formula:

v = rω

where v is the speed of the point, r is its distance from the axis of rotation, and ω is the angular velocity of the disk.

Let's assume that point B is at a distance r from the axis and is moving at a speed v. According to the problem, point A is three times as far from the axis as point B. So, the distance of point A from the axis is 3r.

Since both points are on the same disk, they must have the same angular velocity (ω). Therefore, we can equate their respective speeds:

v(A) = v(B)

Using the formula for the speed of a point on a rotating disk, we get:

r(A)ω = r(B)ω

Substituting r(A) = 3r(B), we get:

3r(B)ω = r(B)ω

Simplifying the equation, we get:

3ω = ω

Therefore, ω can be cancelled out, and we get:

3r(B) = r(A)

So, the speed of point A can be found using the formula:

v(A) = r(A)ω = 3r(B)ω = 3v

Hence, the best choice is B) 3v.

Question 11

You are pedaling a bicycle at 9.8 m/s.The radius of the wheels of the bicycle is 51.9cm.The angular velocity of rotation of the wheels is

Accepted Answer

The answer of You are pedaling a bicycle at 9.8...

Question 12

When an object is moving in a circle at constant speed,its acceleration is

Accepted Answer

The acceleration of an object moving in a circle at constant speed is centripetal acceleration, which is constant in magnitude but always directed towards the center of the circle, thus changing direction as the object moves.

Question 13

A wheel is rotating at 30 rev/min.The angular velocity of the wheel is

Accepted Answer

We know that the formula for angular velocity is:
angular velocity = 2πn
where n is the frequency of rotation (in Hz) or rotations per second.
Since the wheel is rotating at 30 rev/min, we need to convert the frequency to Hz:
30 rev/min = 30/60 Hz = 0.5 Hz
Now, we can use the formula for angular velocity:
angular velocity = 2πn = 2π(0.5) = π rad/s
Therefore, the angular velocity of the wheel is π rad/s, which is equivalent to the answer choice E, F1F1F1S1πF1F1F10 rad/s.

Question 14

Two points,A and B,are on a disk that rotates about an axis.Point A is closer to the axis than point B.Which of the following is not true?

Accepted Answer

Since point A is closer to the axis than point B, it will have a smaller distance to cover in one revolution compared to point B. Therefore, point A will have a smaller angular speed than point B. Hence, option D is not true. Option A is true because point B, being farther from the axis, will cover a greater distance in one revolution and, thus, will have a greater speed. Option B is also true because the centripetal force acting on a point is inversely proportional to its distance from the axis. Since point A is closer to the axis, it will experience a lower centripetal force and, hence, a smaller centripetal acceleration. Option C is true because all points on the rotating disk have the same angular acceleration since they all move with the same angular displacement in the same time interval. Finally, option E is also true because the tangential acceleration of a point on a rotating disk is directly proportional to its radial distance and angular acceleration. Since point A is closer to the axis and has a lower radial distance, it will have a smaller tangential acceleration.

Question 15

You are whirling a stone on the end of a string in a horizontal circle of radius R = 0.65m with a frequency of 4 rev/s when the string breaks.Just after the string breaks,the velocity of the stone is

Accepted Answer

The answer of You are whirling a stone on the...

Question 16

You have a friend who lives in the southern part of the United States,and you live in the northern part.As Earth rotates,your linear velocity is ___________ hers,and your angular velocity is ____________ hers.

Accepted Answer

The answer of You have a friend who lives in...

Question 17

A particle moves uniformly around the circumference of a circle whose radius is 8.0 cm with a period of $\pi$/20 s.The angular velocity $\omega$ of the particle is

Accepted Answer

The angular velocity ω is given by ω = 2π/T, where T is the period. Given T = 0.20 s, ω = 2π/0.20 = 10π ≈ 31.42 rad/s, which is closest to 40 rad/s.

Question 18

Two objects,m₁ and m₂,both of mass m,are place on a horizontal platform which is rotating at a constant angular velocity.m₁ = m is located at a distance R from the axis of rotation and the second object of mass m₂ = 2m is located at a distance 2R.The angular velocity of mass m₁____ to the angular velocity of m₂.

Accepted Answer

Since both objects are on the same platform rotating at a constant angular velocity, their angular velocities are the same regardless of their mass or distance from the axis of rotation.

Question 19

Two objects,m₁ and m₂,both of mass m,are place on a horizontal platform which is rotating at a constant angular velocity.m₁ is located at a distance R from the axis of rotation and m₂ is located at a R.The centripetal acceleration of mass m₁ ____ to the centripetal acceleration of m₂.

Accepted Answer

The answer of Two objects,m₁ and m₂,both of mass m,are...

Question 20

A particle is moving uniformly in a circle of radius 50 cm.Its angular velocity is 96 rad/s.The linear speed of the particle is

Accepted Answer

The linear speed (v) of a particle moving in a circle is given by v = rω, where r is the radius and ω is the angular velocity. Here, r = 0.5 m and ω = 96 rad/s, so v = 0.5 * 96 = 48 m/s.

Quiz 9: Rotation

Two objects,m₁ and m₂,both of mass m,are placed on a horizontal platform which is rotating at a constant angular velocity.m₁ is located at a distance R from the axis of rotation and m₂ is located at a R.The tangential acceleration of mass m₁ ____ to the tangential acceleration of m₂.

The Empire's space station is a long way from any star.It is circular and has a radius of 5.10 km.The angular velocity that is needed to give the station an artificial gravity of 9.80 m/s² at its circumference is

A wheel rotates with a constant nonzero angular acceleration.Which of the following quantities remains constant in magnitude?

Starting from rest,a disk rotates with constant angular acceleration.If it takes 10 rev to reach an angular velocity $\omega$ ,then how many additional revolutions are required to reach an angular velocity 2 $\omega$ ?

The London Eye,which is a giant Ferris wheel,has a diameter of 135 m.It revolves at a constant rate and takes 30 minutes to complete one revolution.What is the linear velocity of a rider in a capsule that is located at the perimeter of the wheel?

A point P is at a distance R from the axis of rotation of a rigid body.The linear speed,centripetal acceleration,and tangential acceleration of the point can be expressed as

A wheel rotates through 6.0 rad in 2.0 s as it is uniformly brought to rest.The initial angular velocity of the wheel before braking began was

A body that moves with a constant speed in a circle

A record turntable rotates through 5.0 rad in 2.8 s as it is accelerated uniformly from rest.What is the angular velocity at the end of that time?

Two points,A and B,are on a disk that rotates about an axis.Point A is three times as far from the axis as point B.If the speed of point B is v,then what is the speed of point A?

You are pedaling a bicycle at 9.8 m/s.The radius of the wheels of the bicycle is 51.9cm.The angular velocity of rotation of the wheels is

When an object is moving in a circle at constant speed,its acceleration is

A wheel is rotating at 30 rev/min.The angular velocity of the wheel is

Two points,A and B,are on a disk that rotates about an axis.Point A is closer to the axis than point B.Which of the following is not true?

You are whirling a stone on the end of a string in a horizontal circle of radius R = 0.65m with a frequency of 4 rev/s when the string breaks.Just after the string breaks,the velocity of the stone is

You have a friend who lives in the southern part of the United States,and you live in the northern part.As Earth rotates,your linear velocity is _ hers,and your angular velocity is __ hers.

A particle moves uniformly around the circumference of a circle whose radius is 8.0 cm with a period of $\pi$ /20 s.The angular velocity $\omega$ of the particle is

Two objects,m₁ and m₂,both of mass m,are place on a horizontal platform which is rotating at a constant angular velocity.m₁ is located at a distance R from the axis of rotation and m₂ is located at a R.The centripetal acceleration of mass m₁ ____ to the centripetal acceleration of m₂.

A particle is moving uniformly in a circle of radius 50 cm.Its angular velocity is 96 rad/s.The linear speed of the particle is

Quiz 9: Rotation

Two objects,m1 and m2,both of mass m,are placed on a horizontal platform which is rotating at a constant angular velocity.m1 is located at a distance R from the axis of rotation and m2 is located at a R.The tangential acceleration of mass m1 ____ to the tangential acceleration of m2.

The Empire's space station is a long way from any star.It is circular and has a radius of 5.10 km.The angular velocity that is needed to give the station an artificial gravity of 9.80 m/s2 at its circumference is

A wheel rotates with a constant nonzero angular acceleration.Which of the following quantities remains constant in magnitude?

Starting from rest,a disk rotates with constant angular acceleration.If it takes 10 rev to reach an angular velocity ω\omegaω ,then how many additional revolutions are required to reach an angular velocity 2 ω\omegaω ?

The London Eye,which is a giant Ferris wheel,has a diameter of 135 m.It revolves at a constant rate and takes 30 minutes to complete one revolution.What is the linear velocity of a rider in a capsule that is located at the perimeter of the wheel?

A point P is at a distance R from the axis of rotation of a rigid body.The linear speed,centripetal acceleration,and tangential acceleration of the point can be expressed as

A wheel rotates through 6.0 rad in 2.0 s as it is uniformly brought to rest.The initial angular velocity of the wheel before braking began was

A body that moves with a constant speed in a circle

A record turntable rotates through 5.0 rad in 2.8 s as it is accelerated uniformly from rest.What is the angular velocity at the end of that time?

Two points,A and B,are on a disk that rotates about an axis.Point A is three times as far from the axis as point B.If the speed of point B is v,then what is the speed of point A?

You are pedaling a bicycle at 9.8 m/s.The radius of the wheels of the bicycle is 51.9cm.The angular velocity of rotation of the wheels is

When an object is moving in a circle at constant speed,its acceleration is

A wheel is rotating at 30 rev/min.The angular velocity of the wheel is

Two points,A and B,are on a disk that rotates about an axis.Point A is closer to the axis than point B.Which of the following is not true?

You are whirling a stone on the end of a string in a horizontal circle of radius R = 0.65m with a frequency of 4 rev/s when the string breaks.Just after the string breaks,the velocity of the stone is

You have a friend who lives in the southern part of the United States,and you live in the northern part.As Earth rotates,your linear velocity is ___________ hers,and your angular velocity is ____________ hers.

A particle moves uniformly around the circumference of a circle whose radius is 8.0 cm with a period of π\piπ /20 s.The angular velocity ω\omegaω of the particle is

Two objects,m1 and m2,both of mass m,are place on a horizontal platform which is rotating at a constant angular velocity.m1 is located at a distance R from the axis of rotation and m2 is located at a R.The centripetal acceleration of mass m1 ____ to the centripetal acceleration of m2.

A particle is moving uniformly in a circle of radius 50 cm.Its angular velocity is 96 rad/s.The linear speed of the particle is

Two objects,m₁ and m₂,both of mass m,are placed on a horizontal platform which is rotating at a constant angular velocity.m₁ is located at a distance R from the axis of rotation and m₂ is located at a R.The tangential acceleration of mass m₁ ____ to the tangential acceleration of m₂.

The Empire's space station is a long way from any star.It is circular and has a radius of 5.10 km.The angular velocity that is needed to give the station an artificial gravity of 9.80 m/s² at its circumference is

Starting from rest,a disk rotates with constant angular acceleration.If it takes 10 rev to reach an angular velocity $\omega$ ,then how many additional revolutions are required to reach an angular velocity 2 $\omega$ ?

You have a friend who lives in the southern part of the United States,and you live in the northern part.As Earth rotates,your linear velocity is _ hers,and your angular velocity is __ hers.

A particle moves uniformly around the circumference of a circle whose radius is 8.0 cm with a period of $\pi$ /20 s.The angular velocity $\omega$ of the particle is

Two objects,m₁ and m₂,both of mass m,are place on a horizontal platform which is rotating at a constant angular velocity.m₁ is located at a distance R from the axis of rotation and m₂ is located at a R.The centripetal acceleration of mass m₁ ____ to the centripetal acceleration of m₂.