In Fig., four pulleys are connected by two belts. Pulley A (radius) is the drive pulley, and it rotates at. Pulley B (radius) is connected by belt to pulley A. Pulley B’ (radius) is concentric with pulley B and is rigidly attached to it. Pulley C (radius) is connected by belt to pulley B’. Calculate (a) the linear speed of a point on belt , (b) the angularspeed of pulley B, (c) the angular speed of pulley B’, (d) the linear speed of a point on belt , and (e) the angular speed of pulley C. (Hint: If the belt between two pulleys does not slip, the linear speeds at the rims of the two pulleys must be equal.)
a) Linear speed of a point on belt is .
b) Angular speed of pulley is .
c) Angular speed of pulley B’ is .
d) Linear speed of point on belt 2 is .
e) Angular speed of pulley C is .
The linear velocity is given as the rate of change of displacement with respect to time. The angular velocity is defined as the rate of change of angular displacement with respect to time. Find the linearvelocity of belt 1 from radius of pulley A and angular speed of pulley A. From linear speed of belt 1, find the remaining values.
The relation between linear and angular velocity is-
where, v is velocity, r is radius and is angular velocity.
Use the following formula to find linear speed,
Hence, linear speed of a point on belt is .
Linear speed of pulley B is also because the belt doesn’t slip.
So, angular speed is given as follows:
Hence, angular speed of pulley is .
Angular speed of pulley is also because it is concentric to pulley A.
Hence, angular speed of pulley B’ is .
Linear speed is given as follows:
Hence, linear speed of point on belt 2 is .
Angular speed is as follows:
Hence, angular speed of pulley C is .
A small ball with mass is mounted on one end of a rod long and of negligible mass. The system rotates in a horizontal circle about the other end of the rod at .
(a) Calculate the rotational inertia of the system about the axis of rotation.
(b) There is an air drag of on the ball, directed opposite its motion. What torque must be applied to the system to keep it rotating at constant speed?
Figure shows a rigid assembly of a thin hoop (of mass m and radius ) and a thin radial rod (of mass m and length ). The assembly is upright, but if we give it a slight nudge, it will rotate around a horizontal axis in the plane of the rod and hoop, through the lower end of the rod. Assuming that the energy given to the assembly in such a nudge is negligible, what would be the assembly’s angular speed about the rotation axis when it passes through the upside-down (inverted) orientation?
Figure 10-36 shows an arrangement of 15 identical disks that have been glued together in a rod-like shape of length L = 1.0000M and (total) mass M = 100.0mg. The disks are uniform, and the disk arrangement can rotate about a perpendicular axis through its central disk at point O . (a) What is the rotational inertia of the arrangement about that axis? (b) If we approximated the arrangement as being a uniform rod of mass M and length L , what percentage error would we make in using the formula in Table 10-2e to calculate the rotational inertia?
In Fig., a small disk of radius has been glued to the edge of a larger disk of radius so that the disks lie in the same plane. The disks can be rotated around a perpendicular axis through point at the center of the larger disk. The disks both have a uniform density (mass per unit volume) of and a uniform thickness of . What is the rotational inertia of the two-disk assembly about the rotation axis through O?
Figure shows a propeller blade that rotates at about a perpendicular axis at point B. Point A is at the outer tip of the blade, at radial distance . (a) What is the difference in the magnitudes a of the centripetal acceleration of point A and of a point at radial distance ? (b) Find the slope of a plot of a versus radial distance along the blade.
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