A wheel of mass M and radius R, which you can approximate as a disk of...
A wheel of mass M and radius R, which you can approximate as a disk of moment of inertiaI= 1/2M R2, is rolling without slipping down an inclined plane.
(a) Draw an extended free-body diagram for the wheel.
(b) After the wheel has dropped a vertical distance h, what is its total kinetic energy?
(c) What fraction of this kinetic energy is translational, and what fraction is rotational?
(d) If instead of rolling down it had been rolling up the incline, would you have had to change the direction of any of the forces in your free-body diagram? If so, which and why? If not, why?
Homework Answers
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A wheel of mass M and radius R, which you can approximate as a
disk of...
6. Consider the system shown: m, J, R The wheel with mass m, radius R, and rotational moment of i...
6. Consider the system shown: m, J, R The wheel with mass m, radius R, and rotational moment of inertia J rolls without slipping down the incline shown. The spring affixed to its axle has rest length h, and is neither extended nor compressed when r 0. The external force F is directed parallel to the direction of rolling. Find the total kinetic energy and potential energy in the system. Assume the gravitational potential energy to be zero when the...
[Use g = 10 m/s^2] A non-uniform wheel of mass 5 kg and moment of inertia...
[Use g = 10 m/s^2] A non-uniform wheel of mass 5 kg and moment of inertia 1/3 mR^2 is set on an incline whose height is h = 4 meters and length is L = 20 meters. The wheel is released from rest at the top of the incline and rolls without slipping to the bottom. What is the wheel's translational kinetic energy at the bottom of the incline? What is the wheel's rotational kinetic energy at the bottom of...
A uniform wheel of mass 10.0 kg and radius 0.400 m is mounted rigidly on an axle through its center
A uniform wheel of mass 10.0 kg and radius 0.400 m is mounted rigidly on an axle through its center (see figure . The radius of the axle is 0.200 m, and the rotational inertia of the wheel-axle combination about its central axis is 0.600 kg·m2. The wheel is initially at rest at the top of a surface that is inclined at angleθ = 43.6o with the horizontal; the axle rests on the surface while the wheel extends into a...
Chapter 11, Problem 081 A uniform wheel of mass 10.0 kg and radius 0.400 m is...
Chapter 11, Problem 081 A uniform wheel of mass 10.0 kg and radius 0.400 m is mounted rigidly on an axle through its center (see the figure). The radius of the axle is 0.200 m, and the rotational inertia of the wheel-axle combination about its central axis is 0.600 kg-m2. The wheel is initially at rest at the top of a surface that is inclined at angle 58.4° with the horizontal; the axle rests on the surface while the wheel...
A solid sphere rolls in released from rest and rolls down an incline plane, which is...
A solid sphere rolls in released from rest and rolls down an incline plane, which is 2.0 m long and inclined at a 30° angle from the horizontal. (a) Find its speed at the bottom of the incline. (Remember that the kinetic energy in rolling motion is the translational kinetic energy ½ Mv2 of the center, plus the rotational K.E. ½ Iω2 about the center. Also remember that v = ωr if the sphere rolls without slipping.) (b) Find the...
Consider a uniform disk of radius R and mass m sliding down an incline making an...
Consider a uniform disk of radius R and mass m sliding down an incline making an angle θ with respect to the horizontal. The coefficient of kinetic friction between the disk and the surface is μk. The torque due to friction causes the disk to rotate as it slides down the incline. a) Compute the linear acceleration of the disk as it slides down the incline. b) Compute the angular acceleration of the disk as it slides down the incline....
A disk with a c value of ½, a mass of 5 kg, and radius of...
A disk with a c value of ½, a mass of 5 kg, and radius of 0.48 meters, rolls without slipping down an incline which has a length of 8 meters and angle of 30 degrees. At the top of the incline, the disk is spinning at 33 rad/s. What is the rotational kinetic energy to the disk at the top of the incline in Joules?
Consider a hoop of radius R and mass M rolling without slipping. Which form of its...
Consider a hoop 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 will have the
same value
D. You need to know
the R of the hoop
E. You need to know
the M of the hoop
anillo "hoop"
We are given a thin wheel of radius r as shown in the figure. The mass...
We are given a thin wheel of radius r as shown in the figure. The mass of the wheel is M and the mass of the spokes is negligible. The wheel rotates about its axis without translational motion at 2 cycles/s. What is the radian frequency of the wheel? If this wheel is now rolling along a road at 3 m/s, then, noting that there is both rotational and translational motion in the wheel, what is its total kinetic energy?
5) A disk with a c value of 1/2, a mass of 10 kg, and radius...
5) A disk with a c value of 1/2, a mass of 10 kg, and radius of 0.57 meters, rolls without slipping down an incline with has a length of 9 meters and angle of 30 degrees. At the top of the incline the disk is spinning at 25 rad/s. What is the rotational kinetic energy of the disk at the bottom of the incline in Joules?
6. Consider the system shown: m, J, R The wheel with mass m, radius R, and rotational moment of inertia J rolls without slipping down the incline shown. The spring affixed to its axle has rest length h, and is neither extended nor compressed when r 0. The external force F is directed parallel to the direction of rolling. Find the total kinetic energy and potential energy in the system. Assume the gravitational potential energy to be zero when the...
[Use g = 10 m/s^2] A non-uniform wheel of mass 5 kg and moment of inertia 1/3 mR^2 is set on an incline whose height is h = 4 meters and length is L = 20 meters. The wheel is released from rest at the top of the incline and rolls without slipping to the bottom. What is the wheel's translational kinetic energy at the bottom of the incline? What is the wheel's rotational kinetic energy at the bottom of...
Chapter 11, Problem 081 A uniform wheel of mass 10.0 kg and radius 0.400 m is mounted rigidly on an axle through its center (see the figure). The radius of the axle is 0.200 m, and the rotational inertia of the wheel-axle combination about its central axis is 0.600 kg-m2. The wheel is initially at rest at the top of a surface that is inclined at angle 58.4° with the horizontal; the axle rests on the surface while the wheel...
Consider a hoop 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 will have the
same value
D. You need to know
the R of the hoop
E. You need to know
the M of the hoop
anillo "hoop"
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