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SSM A uniform wheel of mass 10.0 kg and radius 0.400 m is mounted rigidly on a massless axle through its center (Fig. 11-62). 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 θ = 30.0° with the horizontal; the axle rests on the surface while the wheel extends into a groove in the surface without touching the surface. Once released, the axle rolls down along the surface smoothly and without slipping. When the wheel–axle combination has moved down the surface by 2.00 m, what are (a) its rotational kinetic energy and (b) its translational kinetic energy?
Figure 11-62 Problem 81.
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Chapter 11 Solutions
Fundamentals of Physics, Volume 1, Chapter 1-20
- Figure 10-33 gives angular speed versus time for a thin rod that rotates around one end. The scale on the w axis is set by ws = 6.0 rad/s. (a) What is the magnitude of the rod's angular acceleration? (b) At t = 4.0 s, the rod has rotational kinetic energy of 1.60 J. What is its kinetic energy at t = 0? | t (s) 4 Figure 10-33 Problem 34.arrow_forwardA solid, uniform disk of radius 0.250 m and mass 61.2 kg rolls down a ramp of length 5.10 m that makes an angle of 18.0° with the horizontal. The disk starts from rest from the top of the ramp. (a) Find the speed of the disk's center of mass when it reaches the bottom of the ramp. |m/s (b) Find the angular speed of the disk at the bottom of the ramp. rad/sarrow_forwardA cord is wrapped around the rim of a solid uniform wheel 0.250 m in radius and of mass 9.20 kg. A steady horizontal pull of 40.0 N to the right is exerted on the cord, pulling it off tangentially from the wheel. The wheel is mounted on frictionless bearings on a horizontal axle through its center. (a) Compute the angular acceleration of the wheel and the acceleration of the part of the cord that has already been pulled off the wheel. (b) Find the magnitude and direction of the force that the axle exerts on the wheel. (c) Which of the answers in parts (a) and (b) would change if the pull were upward instead of horizontal?arrow_forward
- The moment of inertia of a solid body about an axis in 3-space relates the angular acceleration about this axis to torque (force twisting the body). The moments of inertia about the coordinate axes of a body of constant density and mass m occupying a region W of volume V are defined to be 1, = +2)av 1, = L+)av m m m (3? + 2) dV V Iy (22 + 2?) dV V (22 V Use these definitions to find the moment of inertia about the z-axis of the rectangular solid of mass 180 given by 0arrow_forward*12-168. A particle travels along the portion of the "four- leaf rose" defined by the equation r= (5 cos 20) m. If the angular velocity of the radial coordinate line is 0=(31²) rad/s, where t is in seconds, determine the radial and transverse components of the particle's velocity and acceleration at the instant = 30°. When t=0,0=0. ① r = (5 cos 20) Prob. 12-168arrow_forwardYou are trying to raise a bicycle wheel of mass m and radius R up over a curb of height h. To do this, you apply a horizontal force F S . What is the smallest magnitude of the force F S that will succeed in raising the wheel onto the curb when the force is applied (a) at the center of the wheel and (b) at the top of the wheel? (c) In which case is less force required?arrow_forwardThe left-hand end of a uniform rod of length L and mass m is attached to a vertical wall by a frictionless hinge. The rod is held at an angle u above the horizontal by a horizontal wire that runs between the wall and the right-hand end of the rod. (a) If the tension in the wire is T, what is the magnitude of the angle u that the rod makes with the horizontal? (b) The wire breaks and the rod rotates about the hinge. What is the angular speed of the rod as the rod passes through a horizontal position?arrow_forwardA cylinder of mass M and radius R is pulled by a constant force of magnitude Fapplied at the top horizontally. The cylinder rolls smoothly on the horizontal surface. Assume that M=10 kg, R=0.10 m, F=12 N, and note that the rotational inertia of the cylinder about its axis is 1/2MR^2 (a) Find the magnitude of the acceleration of thic center of mass of the cylinder (please input the numerical value in unit of m/s) (b) Find the magnitude of the angular acceleration of the contact point between the cylinder and the surface about the axis of the cylinder (please input the numerical value in unit of rad/s). (c) Find the magnitude of the frictional force acting on the cylinder (please input the numerical value in unit of N).arrow_forwardacts on a pebble with position vector 7 = (1.92 m ) – (5.98 m )ê, re ), relative to the origin. What is the resulting torque acting on the pebble about (a) the origin and (b) a point with coordinates (8.32 m, 0, -7.80 m)? Force F = (4.70 N ) - (5.35 Nac (a) Number (b) Number i + i + k Units k Unitsarrow_forwardForce F = (5.58 N)î – (6.71 N )k acts on a pebble with position vector 7 = (2.79 m ) – (7.59 m ) k, relative to the origin. - What is the resulting torque acting on the pebble about (a) the origin and (b) a point with coordinates (3.43 m, 0, -3.30 m)? (a) Number i i k Units (b) Number i i i k Unitsarrow_forwardAs shown in Fig. 10-3, a mass m = 400 g hangs from the rim of a wheel of radius r = 15 cm. When released from rest, the mass falls 2.0 m in 6.5 s. Find the moment of inertia of the wheel. B 400 g mg FT FTarrow_forwardarrow_back_iosarrow_forward_ios
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
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