Ex. 58 : A solid cylinder of uniform density of radius 2 cm has mass 50 g. If its length is 12 cm. Calculate its moment of inertia about an axis passing through its centre and perpendicular to its length.
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- What is the final angular velocity in unit of rad/sec of a solid sphere with radius of 9.78 meters rolls down without slipping a hill of 66.37 meter height, starting from rest? Use g = 9.8 m/s2. The moment of inertia of the solid sphere is 2/5*MR2.Everyone's favorite flying sport disk can be approximated as the combination of a thin outer hoop and a uniform disk, both of diameter Da = 0.273 m. The mass of the hoop part is mh = : 0.120 kg and the mass of the disk part is md = 0.050 kg. Imagine making a boomerang that has the same total moment of inertia around its center as the sport disk. The boomerang is to be constructed in the shape of an "X," which can be approximated as two thin, uniform rods joined at their midpoints. If the total mass of the boomerang is to be m₁ = 0.235 kg, what must be the length Lы of the boomerang? | I Lb = = Cross-sectional view mThe uniform thin rod in the figure below has mass M = 2.50 kg and length L = 2.87 m and is free to rotate on a frictionless pin. At the instant the rod is released from rest in the horizontal position, find the magnitude of the rod's angular acceleration, the tangential acceleration of the rod's center of mass, and the tangential acceleration of the rod's free end. HINT L/2 × CG M O (a) the rod's angular acceleration (in rad/s²) rad/s² (b) the tangential acceleration of the rod's center of mass (in m/s²) (c) m/s² the tangential acceleration of the rod's free end (in m/s²) m/s²
- A playground merry-go-round (a solid disk) has a mass of 120 kg and a radius of 1.80 m and it is rotating with an angular velocity of 0.500 rev/s. What is its angular velocity after a 22.0-kg child (who is initially at rest) gets onto it by grabbing its outer edge? (You can approximate the child as a point mass). (Hint: here you'll need to use the conservation of angular momentum.) a. 0.683 rev/s b. 0.415 rev/s c. 0.366 rev/s d. 0.129 rev/sA 20-kg child running at 1.4 m/s jumps onto a playground merry-go-round that has mass 180 kg and radius 1.6m. She is moving tangent to the platform when she jumps and she lands right on the edge. What is the angular velocity of the child and the merry-go-round if the merry-go-round started from rest? You can treat the merry-go-round as a solid disc and ignore any friction in its axle. Please answer in units of rad/sec.An oversized yo-yo is made from two identical solid disks each of mass M = 2.10 kg and radius R = 10.0 cm. The two disks are joined by a solid cylinder of radius r = 4.00 cm and mass m = 1.00 kg as in the figure below. Take the center of the cylinder as the axis of the system. R. M (a) What is the moment of inertia of the system? Give a symbolic answer. (Use any variable or symbol stated above as necessary.) moment of inertia %3D
- A torque of magnitude 50N · m acts for 3 seconds to start a small airplane propeller (I = 12mr2) of length 1.2m and mass 10kg spinning. If treated as a rod rotated about its center, what is the final angularspeed of the propeller if we neglect the drag on itTwo disks are initially spinning, one above the other on a small axle that provides a small, but non-negligible torque from friction, as shown in the figure below. Both disks have the same radius, R = 2.58 m. Disk 1 has a moment of inertia I1 = 9.8 kg⋅m2. Disk 2 has a moment of inertia I2 = 5 kg⋅ m2. Let vertically up be the z direction, such that counterclockwise rotation as viewed from above corresponds to positive values of the z-component. Disk 1 is initially spinning with a z-component of angular velocity ω1,z = 21 rad/s, and disk 2 is initially spinning with a z-component of angular velocity ω2,z = -15 rad/s. The z component of their common angular velcoity is 8.837 rad/s How much thermal energy is created in the process of disk 1 falling on disk 2 such that they reach a common final angular velocity? You do not need to worry about the gravitational potential energy because the initial separation of the disks is small. I get I need to use kinetic energy equations of 1/2*I*w2 but…a 20 Nm torque acts on a wheel that has 150kgm^2 moment of inertia 1.calculate the angular acceleration of the wheel.