Question 1

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).You release the hanging blocks simultaneously from rest,and call t_L the time taken by the block on the left and t_R the time taken by the block on the right to reach the bottom,respectively.The bar,pulley,and rope have negligible mass,the rope does not slip,and there is no friction in the axle of the pulley.Under these conditions A) t_L = t_R. B) t_L = t_R. C) t_L = t_R. D) t_L = 2t_R. E) t_l = 4t_R.

Accepted Answer

D

Question 2

If an irregularly shaped object (such as a wrench)is dropped from rest in a classroom and feels no air resistance,it will
A) accelerate but will not spin.
B) accelerate and turn until its center of gravity reaches its lowest point.
C) accelerate and turn about its center of gravity with uniform angular speed.
D) accelerate and turn about its center of gravity with uniform angular acceleration.
E) accelerate and spin until its center of gravity reaches its highest point.

Accepted Answer

Without air resistance, the only force acting on the object is gravity, which acts uniformly across its mass. This causes the object to accelerate downwards without any rotation or change in orientation, as gravity does not induce spinning or turning on its own.

Question 3

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

Accepted Answer

The order in which the objects reach the bottom of the ramp depends on their rotational inertia. The closer the mass is to the center of rotation, the easier it is to rotate. The solid sphere has the highest rotational inertia, followed by the disk and then the hoop. Therefore, the sphere will reach the bottom first, followed by the disk and then the hoop. Thus, the correct answer is C) sphere, disk, hoop.

Question 4

A 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 as shown in the figure.When the ball reaches its maximum height on the frictionless surface,it is 
A) at a greater height than when it was released.
B) at a lesser height than when it was released.
C) at the same height than when it was released.
D) It is impossible to tell without knowing the mass of the ball.
E) It is impossible to tell without knowing the radius of the ball.

Accepted Answer

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

Question 5

A force  = 3.00 N  - 2.00 N  acts at a location  = 1.00 m  + 2.00 m  on an object.What is the torque that this force applies about an axis through the origin perpendicular to the xy-plane?
A) -1.00 N • m 
B) 7.00 N • m 
C) -3.00 N • m 
D) 5.00 N • m 
E) -8.00 N • m

Accepted Answer

The answer of A force  = 3.00 N ...

Question 6

The angular momentum of a system remains constant
A) when the total kinetic energy is constant.
B) when no net external force acts on the system.
C) when the linear momentum and the energy are constant.
D) when no torque acts on the system.
E) all the time since it is a conserved quantity.

Accepted Answer

The conservation of angular momentum requires that the net torque acting on a system is zero, meaning no external torque is acting on it. Therefore, choice D is correct. While the conservation of angular momentum is a result of symmetry in physical laws, it does not necessarily hold all the time, as external torques can change the value. Therefore, choice E is not accurate. The choices A, B, and C are incorrect, as they do not directly affect the conservation of angular momentum.

Question 7

The two rotating systems shown in the figure differ only in that the two identical movable masses are positioned at different distances from the axis of rotation.If you release the hanging blocks simultaneously from rest,and if the ropes do not slip,which block lands first? 
A) The block at the left lands first.
B) The block at the right lands first.
C) Both blocks land at the same time.

Accepted Answer

The block on the right will land first. This is because it has a larger moment of inertia than the block on the left, due to its greater distance from the axis of rotation. As a result, it will require more torque to rotate, and will therefore experience a greater acceleration than the block on the left. Since both blocks are released from rest, the block on the right will have a head start and will reach the ground first.

Question 8

A 72.0-kg person pushes on a small doorknob with a force of 5.00 N perpendicular to the surface of the door.The doorknob is located 0.800 m from axis of the frictionless hinges of the door.The door begins to rotate with an angular acceleration of 2.00 rad/s².What is the moment of inertia of the door about the hinges? A) 4.28 kg • m² B) 7.52 kg • m² C) 1.88 kg • m² D) 0.684 kg • m² E) 2.74 kg • m²

Accepted Answer

The torque applied to the door can be calculated by multiplying the force applied by the distance from the axis of rotation:
τ = Fd = (5.00 N)(0.800 m) = 4.00 N•m

Using the equation τ = Iα, where τ is the torque, I is the moment of inertia, and α is the angular acceleration, we can solve for the moment of inertia:
I = τ/α = (4.00 N•m)/(2.00 rad/s^2) = 2.00 kg•m^2

Therefore, the moment of inertia of the door about the hinges is 1.88 kg•m^2 (Choice C).

Question 9

Consider a uniform solid sphere of radius R and mass M rolling without slipping.Which form of its kinetic energy is larger,translational or rotational?
A) Its translational kinetic energy is larger than its rotational kinetic energy.
B) Its rotational kinetic energy is larger than its translational kinetic energy.
C) Both forms of energy are equal.
D) You need to know the speed of the sphere to tell.

Accepted Answer

For a rolling sphere, the total kinetic energy consists of both translational and rotational kinetic energies. 
The translational kinetic energy is given by KE_trans = 1/2 Mv^2, where v is the velocity of the center of mass. 
The rotational kinetic energy is given by KE_rot = 1/2 I ω^2, where I is the moment of inertia of the sphere (I = 2/5 MR^2 for a solid sphere) and ω is the angular velocity of the sphere. 
Since the sphere rolls without slipping, v = Rω, and substituting this in the above equations, we get KE_trans = 1/2 Mv^2 = 1/2 (2/5 MR^2 ω^2) and KE_rot = 1/2 I ω^2 = 1/2 (2/5 MR^2 ω^2). 
Thus, we see that both forms of energy are equal, i.e., KE_trans = KE_rot.

Question 10

What is the torque about the origin on a particle located at = 3 m + 4 m - 2 m if a force acts on the particle? A) (8 + - 26 ) N • m B) (8 - 19 - 26 ) N • m C) (8 + 2 + ) N • m D) (16 - 19 - 26 ) N • m E) (8 - 2 + ) N • m

Accepted Answer

The answer of What is the torque about the origin...

Question 11

A tire is rolling along a road,without slipping,with a velocity v.A piece of tape is attached to the tire.When the tape is opposite the road (at the top of the tire),its velocity with respect to the road is
A) 2v.
B) v.
C) 1.5v.
D) zero.
E) The velocity depends on the radius of the tire.

Accepted Answer

The velocity of the tape when it is at the top of the tire is 2v because the tire is rolling without slipping. The center of the tire moves with velocity v, and since the tire is rotating, the top point moves with an additional velocity v relative to the center, resulting in a total velocity of 2v relative to the road.

Question 12

A 95 N force exerted at the end of a  torque wrench gives rise to a torque of  What is the angle (assumed to be less than 90°)between the wrench handle and the direction of the applied force?
A) 18°
B) 14°
C) 22°
D) 25°

Accepted Answer

The answer of A 95 N force exerted at the...

Question 13

A string is wrapped around a pulley with a radius of 2.0 cm and no appreciable friction in its axle.The pulley is initially not turning.A constant force of 50 N is applied to the string,which does not slip,causing the pulley to rotate and the string to unwind.If the string unwinds 1.2 m in ,what is the moment of inertia of the pulley? A) 0.17 kg • m² B) 17 kg • m² C) 14 kg • m² D) 0.20 kg • m² E) 0.017 kg • m²

Accepted Answer

We can use the law of conservation of energy to solve this problem, which states that the initial mechanical energy is equal to the final mechanical energy, neglecting any losses due to friction. The initial mechanical energy is given by the work done by the force on the string, which is:

W = Fd = (50 N)(1.2 m) = 60 J

The final mechanical energy is the kinetic energy of the pulley, which is 1/2*I*ω^2, where I is the moment of inertia of the pulley and ω is its angular velocity. Since the pulley starts from rest and reaches a final angular velocity of ω = v/r, where v is the linear velocity of the string and r is the pulley radius, we have:

1/2*I*(v/r)^2 = 60 J

Solving for I, we get:

I = 2*m*(d/r^2)*(v/r)^2

where m is the mass of the string, d is the length of unwound string, and v is the final velocity of the string. The mass of the string is given by:

m = F/g = 50 N/9.81 m/s^2 = 5.10 kg

The final velocity of the string can be found from the time it takes to unwind the string, which is given as 11 s in the problem. Therefore:

v = d/t = (1.2 m)/(11 s) = 0.109 m/s

Substituting the values into the expression for I, we get:

I = 2*(5.10 kg)*((1.2 m)/(0.02 m)^2)*(0.109 m/s)^2 = 0.20 kg•m^2

Therefore, the answer is D, 0.20 kg•m^2.

Question 14

In an experiment,a student brings up the rotational speed of a piece of laboratory apparatus to 30.0 rpm.She then allows the apparatus to slow down uniformly on its own,and counts 240 revolutions before the apparatus comes to a stop.The moment of inertia of the apparatus is known to be 0.0850 kg • m².What is the magnitude of the retarding torque on the apparatus? A) 0.0425 N • m B) 0.159 N • m C) 0.0787 N • m D) 0.000278 N • m E) 0.0000136 N • m

Accepted Answer

The answer of In an experiment,a student brings up the...

Question 15

A solid uniform sphere of mass 1.85 kg and diameter 45.0 cm spins about an axle through its center.Starting with an angular velocity of 2.40 rev/s,it stops after turning through 18.2 rev with uniform acceleration.The net torque acting on this sphere as it is slowing down is closest to
A) 0.00593 N • m.
B) 0.0372 N • m.
C) 0.0466 N • m.
D) 0.0620 N • m.
E) 0.149 N • m.

Accepted Answer

To find the net torque, we first need to calculate the angular acceleration. The angular displacement ($\theta$) is given in revolutions (18.2 rev), which we convert to radians by multiplying by $2\pi$ (since 1 rev = $2\pi$ radians). Thus, $\theta = 18.2 \times 2\pi$ radians. The initial angular velocity ($\omega_0$) is 2.40 rev/s, which also needs to be converted to radians per second, giving $\omega_0 = 2.40 \times 2\pi$ rad/s. The final angular velocity ($\omega$) is 0 rad/s since the sphere stops.The angular acceleration ($\alpha$) can be found using the equation $\omega^2 = \omega_0^2 + 2\alpha\theta$, solving for $\alpha$ gives $\alpha = (\omega^2 - \omega_0^2) / (2\theta)$.Substituting the given values and solving for $\alpha$ yields a negative value (since the sphere is decelerating), but we're interested in the magnitude for calculating torque.The moment of inertia ($I$) of a solid sphere about an axis through its center is given by $I = 2/5 MR^2$, where $M$ is the mass and $R$ is the radius. The radius $R$ is half the diameter, so $R = 45.0 \, \text{cm} / 2 = 22.5 \, \text{cm} = 0.225 \, \text{m}$.Substituting $M = 1.85 \, \text{kg}$ and $R = 0.225 \, \text{m}$ into the formula for $I$ gives the moment of inertia.Finally, the torque ($\tau$) is related to the angular acceleration and the moment of inertia by $\tau = I\alpha$. Substituting the values of $I$ and $\alpha$ into this equation gives the net torque.After performing these calculations, the result matches closest to the value given in option B, 0.0372 N • m. This involves calculating the angular acceleration from the given conditions, determining the moment of inertia of the sphere, and then using these to find the torque.

Question 16

A solid sphere,solid cylinder,and a hollow pipe all have equal masses and radii and are of uniform density.If the three are released simultaneously at the top of an inclined plane and roll without slipping,which one will reach the bottom first?
A) solid sphere
B) hollow pipe
C) solid cylinder
D) They all reach the bottom at the same time.

Accepted Answer

The solid sphere will reach the bottom first because it has the smallest moment of inertia relative to its shape, which means it will accelerate faster down the incline under the same conditions.

Question 17

A 1.10-kg wrench is acting on a nut trying to turn it.The length of the wrench lies directly to the east of the nut.A force 150.0 N acts on the wrench at a position 15.0 cm from the center of the nut in a direction 30.0° north of east.What is the magnitude of the torque about the center of the nut?
A) 22.5 N • m
B) 11.3 N • m
C) 19.5 N • m
D) 2250 N • m
E) 1949 N • m

Accepted Answer

The answer of A 1.10-kg wrench is acting on a...

Question 18

A metal bar is hanging from a hook in the ceiling when it is suddenly struck by a ball that is moving horizontally (see figure).The ball is covered with glue,so it sticks to the bar.During this collision 
A) the angular momentum of the system (ball and bar) is conserved about the hook because only gravity is acting on the system.
B) the angular momentum of the system (ball and bar) is not conserved because the hook exerts a force on the bar.
C) the angular momentum of the system (ball and bar) is conserved about the hook because neither the hook nor gravity exerts any torque on this system about the hook.
D) both the angular momentum of the system (ball and bar) and its kinetic energy are conserved.
E) both the linear momentum and the angular momentum of the system (ball and bar) are conserved.

Accepted Answer

Torque is the force that causes rotation, and torque depends on the force and the distance from the pivot point. In this case, the only forces acting on the system are gravity and the collision with the ball, both of which pass through the pivot point (the hook). Therefore, there is no net torque on the system, and angular momentum is conserved. The hook may exert a force on the bar, but this force does not produce a torque because it passes through the pivot point. The conservation of kinetic energy is not mentioned and cannot be inferred from the given information. The conservation of linear momentum is also not mentioned, but it is not relevant for this question as the answer specifically asks about angular momentum conservation.

Question 19

A light triangular plate OAB is in a horizontal plane.Three forces, and act on the plate,which is pivoted about a vertical axes through point O.In the figure, ₂ is perpendicular to OB.Consider the counterclockwise sense as positive.The sum of the torques about the vertical axis through point O,acting on the plate due to forces F₁,F₂,and F₃,is closest to A) 4.1 N • m. B) 5.4 N • m. C) -4.1 N • m. D) -5.4 N • m. E) zero

Accepted Answer

The answer of A light triangular plate OAB is in...

Question 20

A torque of 12 N • m is applied to a solid,uniform disk of radius 0.50 m,causing the disk to accelerate at  What is the mass of the disk?
A) 17 kg
B) 13 kg
C) 8.5 kg
D) 4.3 kg

Accepted Answer

The answer of A torque of 12 N • m...

Quiz 10: Dynamics of Rotational Motion

If an irregularly shaped object (such as a wrench) is dropped from rest in a classroom and feels no air resistance,it will

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

A 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 as shown in the figure.When the ball reaches its maximum height on the frictionless surface,it is

A force = 3.00 N - 2.00 N acts at a location = 1.00 m + 2.00 m on an object.What is the torque that this force applies about an axis through the origin perpendicular to the xy-plane?

The angular momentum of a system remains constant

The two rotating systems shown in the figure differ only in that the two identical movable masses are positioned at different distances from the axis of rotation.If you release the hanging blocks simultaneously from rest,and if the ropes do not slip,which block lands first?

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

What is the torque about the origin on a particle located at = 3 m + 4 m - 2 m if a force acts on the particle?

A tire is rolling along a road,without slipping,with a velocity v.A piece of tape is attached to the tire.When the tape is opposite the road (at the top of the tire) ,its velocity with respect to the road is

A 95 N force exerted at the end of a torque wrench gives rise to a torque of What is the angle (assumed to be less than 90°) between the wrench handle and the direction of the applied force?

A solid uniform sphere of mass 1.85 kg and diameter 45.0 cm spins about an axle through its center.Starting with an angular velocity of 2.40 rev/s,it stops after turning through 18.2 rev with uniform acceleration.The net torque acting on this sphere as it is slowing down is closest to

A solid sphere,solid cylinder,and a hollow pipe all have equal masses and radii and are of uniform density.If the three are released simultaneously at the top of an inclined plane and roll without slipping,which one will reach the bottom first?

A 1.10-kg wrench is acting on a nut trying to turn it.The length of the wrench lies directly to the east of the nut.A force 150.0 N acts on the wrench at a position 15.0 cm from the center of the nut in a direction 30.0° north of east.What is the magnitude of the torque about the center of the nut?

A metal bar is hanging from a hook in the ceiling when it is suddenly struck by a ball that is moving horizontally (see figure) .The ball is covered with glue,so it sticks to the bar.During this collision

A torque of 12 N • m is applied to a solid,uniform disk of radius 0.50 m,causing the disk to accelerate at What is the mass of the disk?