10.6 An extended object consists of two point masses, \( m_{1} \) and \( m_{2} \), connected via a rigid massless rod of length \( L \), as shown in the figure. The object is rotating at a constant angular velocity about an axis perpendicular to the page through the midpoint of the rod. Two time-varying tangential forces, \( F_{1} \) and \( F_{2} \), are applied to \( m_{1} \) and \( m_{2} \), respectively. After the forces have been applied, what will happen to the angular velocity of the object? a) It will increase. c) 't will remain unchanged. b) It will decrease. d) Not enough information is given to make a determination.
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The forces F1 and F2 are tangential to the circular paths of m1 and m2, so they will cause a torque on the system. Show more…
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An extended object consists of two point masses, $m_{1}$ and $m_{2}$, connected via a rigid massless rod of length $L$, as shown in the figure. The object is rotating at a constant angular velocity about an axis perpendicular to the page through the midpoint of the rod. Two time-varying tangential forces, $F_{1}$ and $F_{2}$, are applied to $m_{1}$ and $m_{2}$, respectively. After the forces have been applied, what will happen to the angular velocity of the object? a) It will increase. b) It will decrease. c) It will remain unchanged. d) Not enough information is given to make a determination.
A long, uniform rod of length $L$ and mass $M$ is pivoted about a frictionless, horizontal pin through one end. The rod is released from rest in a vertical position as shown in Figure $P 10.65 .$ At the instant the rod is horizon- tal, find (a) its angular speed, (b) the magnitude of its angular acceleration, (c) the $x$ and $y$ components of the acceleration of its center of mass, and (d) the components of the reaction force at the pivot.
A long, uniform rod of length $L$ and mass $M$ is pivoted about a horizontal, frictionless pin through one end. The rod is released, almost from rest in a vertical position as shown in Figure $\mathrm{P} 10.65$ . At the instant the rod is horizontal, find (a) its angular speed, (b) the magnitude of its angular acceleration, (c) the $x$ and $y$ components of the acceleration of its center of mass, and (d) the components of the reaction force at the pivot.
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