In Fig. 10-23, two forces F → 1 and F → 2 act on a disk that turns about its center like a merry-go-round. The forces maintain the indicated angles during the rotation, which is counterclockwise and at a constant rate. However, we are to decrease the angle θ of F → 1 without changing the magnitude of F → 1 . (a) To keep the angular speed constant, should we increase, decrease, or maintain the magnitude of F → 2 ? Do forces (b) F → 1 and (c) F → 2 tend to rotate the disk clockwise or counterclockwise? Figure 10-23 Question 5.
In Fig. 10-23, two forces F → 1 and F → 2 act on a disk that turns about its center like a merry-go-round. The forces maintain the indicated angles during the rotation, which is counterclockwise and at a constant rate. However, we are to decrease the angle θ of F → 1 without changing the magnitude of F → 1 . (a) To keep the angular speed constant, should we increase, decrease, or maintain the magnitude of F → 2 ? Do forces (b) F → 1 and (c) F → 2 tend to rotate the disk clockwise or counterclockwise? Figure 10-23 Question 5.
Solution Summary: The author explains how to determine the magnitude of the torque caused by each force and accordingly answer the questions.
In Fig. 10-23, two forces
F
→
1
and
F
→
2
act on a disk that turns about its center like a merry-go-round. The forces maintain the indicated angles during the rotation, which is counterclockwise and at a constant rate. However, we are to decrease the angle θ of
F
→
1
without changing the magnitude of
F
→
1
. (a) To keep the angular speed constant, should we increase, decrease, or maintain the magnitude of
F
→
2
? Do forces (b)
F
→
1
and (c)
F
→
2
tend to rotate the disk clockwise or counterclockwise?
A yo-yo is constructed of two brass disks whose thickness b is 8.5mm and whose radius R is 3.5cm, joined by a short axle whose radius Ro is 3.2mm.
A. What is the rotational inertia about its central axis? Neglect rotational inertia of the axle. The density p is 8400kg/m^3.
B. A string of length l=1.1m and of negligible thickness is wound on the axle. What is the linear acceleration of the yo-yo as it rolls down the string from the rest?
In the assembly below the system can rotate around the vertical axis. The left part is a square where R = 0.1 meters, and the mass of each of the four thin bars is uniform and is 0.1 kg. On the left is a massive sphere of radius R = 0.2 meters and Mass M = 0.3 kg. Assume that the system rotates with constant period T = 2.0 s, when, without any external action, as three leftmost bars detach from the system, leaving only the right vertical bar (on the axis) and sphere . What will be the new period of system revolution?
Note: Note that in this case there is no difference between angular velocity and frequency.
Consider the case of a rotating wheel at rest and starting a clockwise rotation, meaning the negative direction of the angular velocity, and increasing (negatively) its value up to -12 rad/sec for 2 seconds. It then maintains a constant velocity for 2 seconds, and then uniformly reduces the magnitude of the velocity for 2 seconds until the wheel is momentarily stopped and restarts its rotation counter clockwise with positive angular velocity, accelerating up to 20 rad/sec in 2 seconds and remaining at a constant rotation for 2 more seconds. Finally, the wheel stops gradually in 2 seconds. Next you can see the graph of angular velocity versus time of this rotation:
Get the slope of the straight line in the range from 4 to 6 seconds and use analytical geometry to build the equation of that line, in the slope-intercept equation form.
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