4.00 kg y 0 2.00 kg 3.00 kg y = 3.00 m X y = -2.00 m y = -4.00 m
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Three small steel balls are connected by rigid, very light rods as shown in the figure. What is the moment of inertia if the object rotates about the x-axis? If we apply a force of 200. N to the most massive ball such that the object will rotate counterclockwise about the x-axis, what
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- A rope with a negligible mass has two blocks that are suspended over a pulley, m, and M, as shown in the image. The pulley can be considered as a uniform solid cylindrical disk. What is the equation for the net torque on the disc? Assume acceleration of blocks are a=(1/2)(9.8m/s2). What is the moment of inertia for this shape? (using the net torque equation from the above question, substitute the moment of inertia) The angular acceleration is correlated to the linear acceleration as α=r. Make the substitution into the torque equation in order to get the equation in terms of acceleration, α only.A disk of radius R and thickness t has a mass density that increases from the center outward, given by p = po (r/R), where r is the distance from the axis of the disk. What is the moment of inertia about the disk axis in terms of M and R? O MR 2MR O sMP 3MR 5 O 2MR 3 5MR 3F3
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- rod of length L = .9 m and mass mod = .1 kg connects two small balls of mass m = .2 kg each. The rod rotates about its midpoint with an axis perpendicular to the rod. The initial angular velocity is w, = 3 rad/s in the counterclockwise direction. A tangential force F = 9 N is applied to one of the spheres for 2 s causing the system to Rotation accelerate. a. What is the moment of inertia of the rod and ball m system? b. What is the torque acting on the system? Magnitude and direction? c. What is the angular acceleration of the system? d. What is the final angular velocity of the rod? e. What is the final speed v of one of the masses?2.5 3. A playground merry-go-round of radius 1.5 meters. The child applies a constant force of F, =50 Newtons to the rim. There is a frictional torque of 35 Nm opposing the rotation. The graph shows a plot of the resulting angular velocity of the merry-go-round as a function of time. 2 1.5 0.5 Fo view from above time (s) a. What is the torque due to the force F, (take ccw as positive)? b. What is the moment of inertia of the merry-go-round? @ (rad/sec)Three point objects with masses ?1=2.6 kg, ?2=4.0 kg,and ?3=0.90 kg are arranged in the configuration shown in the figure. The distance to mass ?1 is ?1=25 cm and the distance to mass ?3 is ?3=41 cm. The distances are measured from the axis ?. What is the combined moment of inertia ? for the three point objects about the axis ? ?
- Three point objects with masses ?1=2.1 kg, ?2=2.9 kg, and ?3=1.7 kg are arranged in the configuration shown in the figure. The distance to mass ?1 is ?1=22 cm and the distance to mass ?3 is ?3=42 cm. The distances are measured from the axis ?. What is the combined moment of inertia ? for the three point objects about the axis ? ?Wile E. Coyote wants to flatten the Road Runner. Wile E. puts food at a pre-determined distance from the edge of a cliff. While the Road Runner eats the food, Wile E. pushes a log down the hill. It rolls without slipping. The radius of the log is 0.3 m. The mass of the log is 80 kg. The rotational inertia of the log is given by I = ½ MR2 . The translational speed of the log just before it leaves the cliff horizontally is 16 m/s. The Road Runner is 10 m below the cliff. If the log is to successfully hit the Road Runner, the food must be place at a precise location from the base of the cliff which you will determine. a. Use only energy considerations and the fact that the log does not slip as it rolls to determine the height it started from, h, before it went over the cliff. b. Determine how far from the edge of the cliff the food needs to be placed so the log lands on the Road Runner. The rotating motion of the log in the air does not affect the motion of the log once it is in the air.…A soccer player extends her lower leg in a kicking motion by exerting a force with the muscle above the knee in the front of her leg. Suppose she produces an angular acceleration of 32.5 rad/s2 and her lower leg has a moment of inertia of 0.75 kg⋅m2 . What is the force, in newtons, exerted by the muscle if its effective perpendicular lever arm is 2.1 cm? F =