Ex/7: The kinetic energy of rotation of a body about a given axis is 157 J. It angular momentum about the same axis is 12.5 kg-m². Find the frequency of rotation of the body and moment of inertia about the given axis.
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- A sanding disk with rotational inertia 9.8 x 103 kg-m² is attached to an electric drill whose motor delivers a torque of magnitude 35 N-m about the central axis of the disk. About that axis and with torque applied for 14 ms, what is the magnitude of the (a) angular momentum and (b) angular velocity of the disk? (a) Number i Units (b) Number i UnitsJoe's shoulder is labeled S and two points on the cable are labeled P and B. The coordinates of the three points are given below and the tension in the cable is 200 N. Find the moment about Joe's shoulder. Point S P B X (m) 0.68 0 1.9 Y (m) 0.9 3.2 1.1 z (m) 1.4 0 1.4In figure skating, kelen rotated at an angular speed of 9.04 rad/s with her arms pulled in. At the arena, watching her performance, a graduate student calculated that her moment of inertia with arms pulled in was 3.05 kmg^2. After 45 seconds, kelen extends her arms, and her angular speed changed to 4.37 rad/s. What is kelens new moment of inertia?
- Multiple-Concept Example 10 reviews the approach and some of the concepts that are pertinent to this problem. The figure shows a model for the motion of the human forearm in throwing a dart. Because of the force M applied by the triceps muscle, the forearm can rotate about an axis at the elbow joint. Assume that the forearm has the dimensions shown in the figure and a moment of inertia of 0.077 kg-m2 (including the effect of the dart) relative to the axis at the elbow. Assume also that the force M acts perpendicular to the forearm. Ignoring the effect of gravity and any frictional forces, determine the magnitude of the force M needed to give the dart a tangential speed of 3.1 m/s in 0.13 s, starting from rest. 0.28 m Axis at elbow joint 0.025 m Number i UnitsDivers change their body position in midair while rotating about their center of mass. In one dive, the diver leaves the board with her body nearly straight, then tucks into a somersault position. If the moment of inertia of the diver in a straight position is 14 kg ⋅ m2 and in a tucked position is 4.0 kg ⋅ m2, by what factor does her angular speed increase?I drive a Nissan Leaf to work. With the e-pedal on, the motor recovers energy through braking very aggressively. I need about 7 KW-hour to come to school if I use mostly the freeways. That’s about 5 KW-hour if I take mostly local streets. From the energy perspective, can you offer an explanation to explain this difference?
- 6.Multiple-Concept Example 10 reviews the approach and some of the concepts that are pertinent to this problem. The figure shows a model for the motion of the human forearm in throwing a dart. Because of the force M applied by the triceps muscle, the forearm can rotate about an axis at the elbow joint. Assume that the forearm has the dimensions shown in the figure and a moment of inertia of 0.062 kg-m? (including the effect of the dart) relative to the axis at the elbow. Assume also that the force M acts perpendicular to the forearm. Ignoring the effect of gravity and any frictional forces, determine the magnitude of the force M needed to give the dart a tangential speed of 4.5 m/s in 0.14 s, starting from rest. 0.28 m Axis at elbow joint 0.025 m Number i UnitsFour identical particles (mass of each = 0.40 kg) are placed at the vertices of a rectangle (2.0 m × 3.0 m) and held in those positions by four light rods which form the sides of the rectangle. What is the moment of inertia of this rigid body about an axis that passes through the mid-points of the longer sides and is parallel to the shorter sides? Group of answer choices 2.7 kg⋅m2 3.6 kg⋅m2 1.6 kg⋅m2 3.1 kg⋅m2 4.1 kg⋅m2
- A turntable s pins on a frictionless bearing. Its moment of inertia is 3.00 x 10-2 kg m2. It initially rotates at 25.0 rev/min about an axis through its center. Then, a 0.6-kg ball of putty is dropped vertically onto the turntable. It lands and sticks at a point 0.10 m from the center. By what factor does this collision change the angular momentum of the system? That is, Lafter = [factor] x Lpefore- (Hint: Since it moves vertically the putty has initial angular momentum of zero.) O a. 1.22 b.0.820 c. 1.00 (no change) d. 1.20Physics Angular MotionA 10 kg wheel with a 0.4 meter radius is rotating at 4 rad/s. A 8 Nm torque is applied to the wheel. The rotational inertia of the wheel is 0.48 kgm2. The angular momentum of the wheel changes by 4 kg*m2/s. How long was the torque applied to the wheel.