6. A solid, uniform bowling ball (mass 5.5 kg and radius 15 cm) starts at rest at the top of an incline of height 3.3 m and rolls without slipping. The angle of the incline is set so the acceleration of the bowling ball is 0.98 m/s?. (a) What is the angular speed of the bowling ball at the bottom of the incline?
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- A uniform solid disk of radius 3 m and mass 2.0 kg rolls without slipping. to the bottom of an inclined plane. If the angular velocity of the disk is 8 rd/s at the bottom, what is the height of the inclined plane? 22m 19.71m None of the above 6.73m 44.1 m/sA 39.8 kg child stands on a spinning platform that has been well maintained (neglect friction in the axle). Initially the platform is spinning at 4.9 rev/s while the child's arms are extended outward (holding some weights). The child then pulls the weights back to close to their body. What is the final angular speed in rev/s of the platform? Assume that the child can be considered a cylinder with a diameter of 1.2 m, spinning along its center axis and the weights are point masses (2 kg each) that are initially 1.1 m away from the center of the child. Assume that the weights are at the outer edge of the "cylinder" (i.e., the child) in the final moment.A 10 kg cylindrical barrel with a radius of 0.5 m rotates about a vertical axis of rotation without displacing with an initial angular velocity of 4 rad/s. The rotational inertia of the cylindrical barrel is 0.3mr2 and rain begins to fill the barrel with water as its rotating. If the barrel accumulates 4 kg of water, calculate the new angular velocity of the barrel.
- 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?27. A bicyclist starting at rest produces a constant angular acceleration of 1.70 rad/s2 for wheels that are 34.0 cm in radius. (a) What is the bicycle's linear acceleration (in m/s2)? (Enter the magnitude.) (b) What is the angular speed of the wheels (in rad/s) when the bicyclist reaches 11.2 m/s? (c) How many radians have the wheels turned through in that time? (d) How far (in m) has the bicycle traveled?
- A diver performs a flip in the air. The radius of gyration is 0.43 when the diver initially leave the board and the diver is rotating at an angular velocity of 6.3 rad/sec. What is the linear velocity of the head when they decrease their radius of gyration to 0.24. The distance from the head to the center of gravity of the individual is 0.3 meters?A 10 kg cylindrical barrel with a radius of 0.5 m rotates about a vertical axis of rotation without displacing with an initial angular velocity of 4 rad/s. The rotational inertia of the cylindrical barrel is 0.3mr2 and rain begins to fill the barrel with water as its rotating. If the barrel accumulates 4 kg of water, calculate the new angular velocity of the barrel.A solid ball (sphere) of mass 1 kg and radius 0.3 m is held at rest at the top of a ramp. There is enough friction so that the ball will roll down the ramp without slipping. The top of the ramp is 10 meters above the ground.What will the speed be of the ball just before it hits the bottom of the ramp?
- A ceiling fan can accelerate from rest to 2pi rad/s in 8 seconds. (A) what is the angular acceleration of the fan? (B) find the angular displacement of the fan during the first 5 seconds. (C) at the full angular speed of 2pi rad/s find the corresponding tangential speed of a point at the rim of the wing if the radius of the wing is r=0.5m. (D) what is the centripetal acceleration of a point at the rim (r=0.5 m) when the fan reaches full speed? can you give detailed steps please?Starting from rest, a hollow ball rolls completely down a hill of height 3.5 meters. At the bottom the ball has an angular velocity of 20.2 rad/s. Calculate the radius of the ball. (Iball = (2/3)mr2) (Assume that no energy is lost due to nonconservative forces.)The tires on a car have a diameter of 0.70 m. If the car moves in a straight line with a speed of 25.2 km/h through a level parking lot, what is the angular speed of the tires?