Question 1

Two children,Ahmed and Jacques,ride on a merry-go-round.Ahmed is at a greater distance from the axis of rotation than Jacques.Which of the following are true statements? (There could be more than one correct choice. )

Accepted Answer

B) When two points (in this case, Ahmed and Jacques) are on the same rotating object (the merry-go-round), they share the same angular speed because they complete a rotation in the same amount of time, regardless of their distance from the axis of rotation.D) Ahmed, being at a greater distance from the axis of rotation, has a greater tangential speed than Jacques. Tangential speed increases with distance from the axis of rotation, given by the formula $v = r\omega$, where $v$ is the tangential speed, $r$ is the radius (distance from the axis), and $\omega$ is the angular speed.

Question 2

A disk,a hoop,and a solid sphere are released at the same time at the top of an inclined plane.They are all uniform and roll without slipping.In what order do they reach the bottom?

Accepted Answer

The solid sphere will reach the bottom first as it has the smallest moment of inertia and will therefore accelerate faster down the inclined plane. The disk will reach the bottom next as it has a higher moment of inertia than the sphere but lower than the hoop. The hoop will reach the bottom last as it has the highest moment of inertia and will be the slowest to accelerate down the inclined plane. Thus, the order of arrival at the bottom is sphere, disk, hoop.

Question 3

When a rigid object rotates about a fixed axis,what is true about all the points in the object? (There could be more than one correct choice. )

Accepted Answer

All points on a rigid object rotating about a fixed axis have the same angular speed and angular acceleration because these quantities are properties of the entire object, not individual points.

Question 4

A solid sphere,solid cylinder,and a hollow pipe all have equal masses and radii.If the three of them are released simultaneously at the top of an inclined plane and do not slip,which one will reach the bottom first?

Accepted Answer

The solid sphere will reach the bottom first because it has the smallest moment of inertia among the three, which means it will have the highest acceleration down the incline.

Question 5

Consider a uniform hoop of radius R and mass M rolling without slipping.Which is larger,its translational kinetic energy or its rotational kinetic energy?

Accepted Answer

For a uniform hoop rolling without slipping, the translational kinetic energy and the rotational kinetic energy are equal. This is a consequence of the parallel-axis theorem. Therefore, both kinetic energies have the same value: K = (1/2)MV^2 + (1/2)Iω^2, where V is the speed of the hoop's center of mass, ω is the angular speed of the hoop, M is the mass of the hoop, and I is the moment of inertia of the hoop about an axis passing through its center of mass.

Question 6

The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left),or a distance r/2 from the axis of rotation (right).If you release the hanging blocks simultaneously from rest,

Accepted Answer

The time period of a simple pendulum is given by T= 2π√(l/g), where T is the time period, l is the length of the pendulum, and g is the acceleration due to gravity.

For the system on the left, the effective length of the pendulum is r, as the bob moves in a circular path of radius r. 
For the system on the right, the effective length of the pendulum is r/2.

We know that the time period of the pendulum increases as its length increases. Therefore, the pendulum on the left would have a longer time period than the pendulum on the right, and consequently, take longer to complete one oscillation.

Since both pendulums start from rest, the pendulum on the right would complete its first oscillation faster and the block attached to it would touch the ground first. Therefore, the answer is B.

Question 7

When a fan is turned off,its angular speed decreases from 10 rad/s to 6.3 rad/s in 5.0 s.What is the magnitude of the average angular acceleration of the fan?

Accepted Answer

The answer of When a fan is turned off,its angular...

Question 8

A chicken is running in a circular path with an angular speed of 1.52 rad/s.How long does it take the chicken to complete one revolution?

Accepted Answer

To complete one revolution (360 degrees or 2π radians), the time taken (T) can be calculated using the formula T = 2π/ω, where ω is the angular speed. Substituting ω = 1.52 rad/s, T = 2π/1.52 = 4.13 s.

Question 9

Two uniform solid balls,one of radius R and mass M,the other of radius 2R and mass 8M,roll down a high incline.They start together from rest at the top of the incline.Which one will reach the bottom of the incline first?

Accepted Answer

For rolling objects, the acceleration down an incline does not depend on the mass or the radius of the object but on the gravitational acceleration and the incline angle. Both spheres will have the same acceleration and thus reach the bottom at the same time.

Question 10

Through how many degrees does a 33 rpm turntable rotate in

Accepted Answer

The answer of Through how many degrees does a 33...

Question 11

At a certain instant,a compact disc is rotating at 210 rpm.What is its angular speed in rad/s?

Accepted Answer

To convert revolutions per minute (rpm) to radians per second (rad/s), use the conversion factor $2\pi$ rad/rev and the fact that there are 60 seconds in a minute. Thus, $210 \, \text{rpm} = 210 \times \frac{2\pi}{60} \, \text{rad/s} = 22 \, \text{rad/s}$.

Question 12

Consider a solid uniform sphere of radius R and mass M rolling without slipping.Which form of its kinetic energy is larger,translational or rotational?

Accepted Answer

For a solid sphere rolling without slipping, the translational kinetic energy (1/2)Mv^2 is larger than the rotational kinetic energy (1/2)Iω^2, where I = (2/5)MR^2 and ω = v/R. Substituting I and ω, the rotational kinetic energy becomes (1/5)Mv^2, which is less than the translational kinetic energy.

Question 13

Suppose a uniform solid sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest.The linear velocity of the sphere at the bottom of the incline depends on

Accepted Answer

The linear velocity of a sphere rolling without slipping down an incline depends on the height from which it starts and the acceleration due to gravity, not on its mass or radius. This is because both the translational kinetic energy and rotational kinetic energy it gains are independent of its mass and radius when considering the conservation of energy and the moment of inertia for a solid sphere.

Question 14

Suppose a solid uniform sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest.The angular velocity of the sphere at the bottom of the incline depends on

Accepted Answer

The angular velocity of the sphere at the bottom of the incline only depends on the radius of the sphere. This can be derived from the conservation of energy principle, where the potential energy at the top of the incline is converted into both kinetic energy of translation and rotational kinetic energy at the bottom of the incline. Since the sphere is rolling without slipping, the kinetic energy of translation is related to the rotational kinetic energy through a factor of (2/5)MR^2, where M is the mass and R is the radius of the sphere. Therefore, the final angular velocity is proportional to the square root of the ratio of the rotational kinetic energy to (2/5)MR^2, which only depends on the radius of the sphere.

Question 15

A solid sphere and a solid cylinder,both uniform and of the same mass and radius,roll without slipping at the same forward speed.It is correct to say that the total kinetic energy of the solid sphere is

Accepted Answer

The answer of A solid sphere and a solid cylinder,both...

Question 16

What is the angular speed,in rad/s,of a flywheel turning at 813.0 rpm?

Accepted Answer

Angular speed is measured in radians per second (rad/s). To convert from revolutions per minute (rpm) to radians per second, we use the conversion factor:
1 rpm = (2π/60) rad/s
where 2π is the number of radians in one revolution, divided by 60 seconds per minute. 
So, angular speed (ω) in radians per second is given by:
ω = (2π/60) × rpm
ω = (2π/60) × 813.0 rpm 
ω = 85.14 rad/s (rounded to two decimal places)

Question 17

A disk and a hoop of the same mass and radius are released at the same time at the top of an inclined plane.If both are uniform,which one reaches the bottom of the incline first if there is no slipping?

Accepted Answer

Both the disk and the hoop will have the same gravitational potential energy at the top of the incline. As there is no slipping, both will reach the bottom of the incline with the same kinetic energy. However, the moment of inertia of a hoop is greater than that of a disk (I_hoop = MR^2 and I_disk = (1/2)(MR^2)), which means that the hoop has a greater resistance to rotational motion (i.e., harder to start and stop rotating). Therefore, the hoop will take longer to roll down the incline compared to the disk, which will reach the bottom first.

Question 18

A uniform ball is released from rest on a no-slip surface,as shown in the figure.After reaching its lowest point,the ball begins to rise again,this time on a frictionless surface.When the ball reaches its maximum height on the frictionless surface,it is

Accepted Answer

The answer of A uniform ball is released from rest...

Question 19

A small uniform disk and a small uniform sphere are released simultaneously at the top of a high inclined plane,and they roll down without slipping.Which one will reach the bottom first?

Accepted Answer

Both the disk and the sphere have the same potential energy at the top of the inclined plane due to the same height and mass. However, the sphere has a larger moment of inertia than the disk, which means that it will have a greater rotational inertia and slower acceleration down the inclined plane. Therefore, the disk will reach the bottom before the sphere does.

Question 20

The figure shows scale drawings of four objects,each of the same mass and uniform thickness,with the mass distributed uniformly.Which one has the greatest moment of inertia when rotated about an axis perpendicular to the plane of the drawing at point P?

Accepted Answer

The answer of The figure shows scale drawings of four...

Quiz 10: Rotational Kinematics and Energy