Question: A uniform, thin, solid door has height 2.20 m, width 0.870 m, and mass 23.0 kg. (a) Find its moment of inertia for rotation on its hinges. (b) Is any piece of data unnecessary?
(a)The moment of inertia for rotation on its hinges is
(b)The piece of unnecessary data is height.
Moment of inertia about a given axis of rotation resists a change in its rotational motion; it can be regarded as a measure of rotational inertia of the body.
L (width of the floor)
H (height of door)
The door can be modeled as long, thin rod with rotation axis through end, .
Substituting the numerical values, we get
So, the answer is .
The height of the door is the unnecessary piece of data.
So, the answer is height of the door.
Question: Figure P10.41 shows a side view of a car tire before itis mounted on a wheel. Model it as having two side-walls of uniform thickness 0.635 cm and a tread wall of uniform thickness 2.50 cm and width 20.0 cm. Assume the rubber has uniform density 1.10 3 103 kg/m3. Find its moment of inertia about an axis perpendicular to the page through its center.
An ice skater starts a spin with her arms stretched out to the sides. She balances on the tip of one skate to turn without friction. She then pulls her arms in so that her moment of inertia decreases by a factor of 2. In the process of her doing so, what happens to her kinetic energy? (a) It increases by a factor of 4. (b) It increases by a factor of 2. (c) It remains constant. (d) It decreases by a factor of 2. (e) It decreases by a factor of 4.
Question: The four particles in Figure P10.45 are connected by rigid rods of negligible mass. The origin is at the center of the rectangle. The system rotates in the x y plane about the z axis with an angular speed of 6.00 rad/s. Calculate (a) the moment of inertia of the system about the z axis and (b) the rotational kinetic energy of the system.
Two children are playing with a roll of paper towels.One child holds the roll between the index fingersof her hands so that it is free to rotate, and the second child pulls at constant speed on the free end ofthe paper towels. As the child pulls the paper towels,the radius of the roll of remaining towels decreases.
(a) How does the torque on the roll change with time?(b) How does the angular speed of the roll change in time? (c) If the child suddenly jerks the end paper towel with a large force, is the towel more likely to break from the others when it is being pulled from an early full roll or from a nearly empty roll?
A ball having mass m is fastened at the end of a flagpole that is connected to the side of a tall building at point Pas shown in Figure. The length of the flagpole is, and it makes an angle with the x-axis. The ball becomes loose and starts to fall with acceleration . (a) Determine the angular momentum of the ball about point Pas a function of time. (b) For what physical reason does the angular momentum change? (c) What is the rate of change of the angular momentum of the ball about point P?
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