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Complete revolutions

Consider a point on a bicycle wheel as the wheel makes exactly four complete revolutions about a fixed axis. Compare the linear and angular displacement of the point. When a point on the rim of a 0.30-m-radius wheel experiences a centripetal acceleration of 4.0 m/s2, what tangential acceleration does that point experience? A wheel is rotated about a horizontal axle at a constant angular speed. Next it is rotated in the opposite direction with the same angular speed. The acceleration at a point on the top of the wheel in the second case as compared to the acceleration in the first case: A rod of length L is pivoted about its left end and has a force F applied perpendicular to the other end. The force F is now removed and another force F’ is applied at the midpoint of the rod. If F’ is at an angle of 30° with respect to the rod, what is its magnitude if the resulting torque is the same as when F was applied A solid cylinder (I = MR2/2) has a string wrapped around it many times. When I release the cylinder, holding on to the string, the cylinder falls and spins as the string unwinds. What is the downward acceleration of the cylinder as it falls? A 40-kg boy is standing on the edge of a stationary 30-kg platform that is free to rotate. The boy tries to walk around the platform in a counterclockwise direction. As he does An automobile accelerates from zero to 30 m/s in 6.0 s. The wheels have a diameter of 0.40 m. What is the average angular acceleration of each wheel? the average angular acceleration ? = ?’ – ?0 / t ? = ?’ / t ?’ – is the final angular velocity we know = v = r? ? = v /r = 30 / 0.20 m now ? = 30 / 0.20 m * 6 = 25 rads /sec^2A bucket of water with total mass 23 kg is attached to a rope, which in turn is wound around a 0.050-m radius cylinder, with crank, at the top of a well. The moment of inertia of the cylinder and crank is 0.12 kg?m2. The bucket is raised to the top of the well and released to fall back into the well. What is the kinetic energy of the cylinder and crank at the instant the bucket is moving with a speed of 8.0 m/s?T = 152.38 N (not simply m*g = 225.4 N)a = F/m = [mg – T]/m = 3.174 m/s²A gyroscope has a moment of inertia of 0.14 kg?m2 and an initial angular speed of 15 rad/s. Friction in the bearings causes its speed to reduce to zero in 30 s. What is the value of the average frictional torque? A turntable has a moment of inertia of 3.00 × 10?2 kg?m2 and spins freely on a frictionless bearing at 25.0 rev/min. A 0.300-kg ball of putty is dropped vertically onto the turntable and sticks at a point 0.100 m from the center. What is the new rate of rotation of the system? A copper wire of length 2.0 m, cross sectional area 7.1 × 10?6 m2 and Young’s modulus 11 × 1010 N/m2 has a 200-kg load hung on it. What is its increase in length? (g = 9.8 m/s2) What is the total force on the bottom of a 2.0-m-diameter by 1.0-m-deep round wading pool due to the weight of the air and the weight of the water? (Note the pressure contribution from the atmosphere is 1.0 × 105 N/m2, the density of water is 1 000 kg/m3, and g = 9.8 m/s2.) A 15 000-N car on a hydraulic lift rests on a cylinder with a piston of radius 0.20 m. If a connecting cylinder with a piston of 0.040-m radius is driven by compressed air, what force must be applied to this smaller piston in order to lift the car? Dams at two different locations are needed to form a lake. When the lake is filled, the water level will be at the top of both dams. The Dam #2 is twice as high and twice as wide as Dam #1. How much greater is the force of the water on Dam #2 than the force on Dam #1? (Ignore atmospheric pressure; it is pushing on both sides of the dams.) A piece of aluminum has density 2.70 g/cm3 and mass 775 g. The aluminum is submerged in a container of oil (oil’s density = 0.650 g/cm3). How much oil does the metal displace? A block of wood has density 0.50 g/cm3 and mass 1 500 g. It floats in a container of oil (the oil’s density is 0.75 g/cm3). What volume of oil does the wood displace? Think of Bernoulli’s equation as it pertains to an ideal fluid flowing through a horizontal pipe. Imagine that you take measurements along the pipe in the direction of fluid flow. What happens to the sum of the pressure and energy per unit volume?

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