A solid cylinder of uniform density of radius 2 cm has mass of 50 g. If its length is 10 cm, Calculate its moment of inertia about (i) its own axis of rotation passing through the centre. (ii) an axis passing through its centre and perpendicular to its length.
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- A torque of 36.2 N · m is applied to an initially motionless wheel which rotates around a fixed axis. This torque is the result of a directed force combined with a friction force. As a result of the applied torque the angular speed of the wheel increases from 0 to 10.5 rad/s. After 6.10 s the directed force is removed, and the wheel comes to rest 61.0 s later. (a) What is the wheel's moment of inertia (in kg · m2)? kg • m m2 (b) What is the magnitude of the torque caused by friction (in N m)? N. m (c) From the time the directed force is initially applied, how many revolutions does the wheel go through? revolutionsA disk of mass M is spinning freely at 9.27 rad/s when a second identical disk, initially not spinning, is dropped onto it so that their axes coincide. In a short time the two disks are corotating. HINT (a) What is the angular speed of the new system (in rad/s)? rad/s (b) If a third such disk is dropped on the first two, find the final angular speed of the system (in rad/s). rad/sA robot wheel rotates with a constant angular speed of 3.8 rad/s. The radius of the robot wheel is radius = 0.4 meters. Find the following: a) angular displacement of the robot wheel at a time of 7 seconds. b) linear (tangential) speed of a point on the rim.
- A wheel accelerates with a constant angular acceleration of 2 rad/s2. If the initial angular velocity is 4.0 rad/s, (a) what is the angular velocity at t = 5.0 s? (b) What is the angle the wheel rotates through in 5.0 s? (c) If the torque added to the wheel is 15 Nm, what is the moment of inertia of this wheel?Consider a person who is sitting on a frictionless rotating stool. The person initially has his arms outstretched and is rotating with an angular speed of 5.0 rad/s. He then pulls his arms close to his body, thus reducing his moment of inertia to 80% of the initial one. What is his final angular speed?An electric motor rotating a workshop grinding wheel at 1.08 x 10 rev/min is switched off. Assume the wheel has a constant negative angular acceleration of magnitude 2.06 rad/s? (a) How long does it take the grinding wheel to stop? Note that the time required for the wheel to stop is the same as the time for the wheel to start from rest and reach the given angular speed with the same magnitude angular acceleration, s (b) Through how many radians has the wheel turned during the time interval found in part (a)? It might be helpful to translate this problems into linear variables (a car traveling with an initial speed and then slowing down with a constant negative acceleration), rad Need Help? Road Master
- Problem 2: A wheel with radius r= 1.8 m has a tangential force F = 14.2 N acting on it as shown. F Part (a) What is the magnitude of the torque about the center of the wheel, in N•m? N•m sin() cos() tan() 7 8 9 НОMЕ cotan() asin() acos() E ↑^^| 4 5 6. atan() acotan() sinh() 1 3 cosh() tanh() cotanh() END O Degrees Radians VO BACKSPАСЕ DEL CLEAR Part (b) What is the direction of the torque?A disk rotates about its central axis starting from rest and accelerates with constant angular acceleration. At one time it is rotating at 8.70 rev/s; 35.0 revolutions later, its angular speed is 20.0 rev/s. Calculate (a) the angular acceleration (rev/s2), (b) the time required to complete the 35.0 revolutions, (c) the time required to reach the 8.70 rev/s angular speed, and (d) the number of revolutions from rest until the time the disk reaches the 8.70 rev/s angular speed. Unit (a) Number (b) Number Unit (c) Number Unit (d) Number UnitThe wheels of a wagon can be approximated as the combination of a thin outer hoop, of radius ʼn = 0.315 m and mass 4.32 kg, and two thin crossed rods of mass 7.80 kg each. A farmer would like to replace his wheels with uniform disks ta = 0.0588 m thick, made out of a material with a density of 7370 kg per cubic meter. If the new wheel is to have the same moment of inertia about its center as the old wheel about its center, what should the radius of the disk be? ℗ la ro rd = m
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