In the figure, a solid cylinder of radius 6.0 cm and mass 14 kg starts from rest and rolls without slipping a distance L = 7.9 m down a roof that is inclined at angle 0 = 35°. (a) What is the angular speed of the cylinder about its center as it leaves the roof? (b) The roof's edge is at height H = 3.8 m. How far horizontally from the roof's edge does the cylinder hit the level ground? (a) Number (b) Number L i 0 H 119.737 M Units rad/ Units m
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- A solid sphere with a mass of 2.00 kg and a radius of 50.0 cm is rolled towards the bottom of a ramp. When the sphere reaches the bottom of the ramp, a point halfway between the center of the sphere and the edge of the sphere has a tangential speed of 1.50 m/s. How high up the ramp will the sphere roll?A small fan has blades that have a radius of 0.0600 m. When the fan is turned on, the tips of the blades have a tangential acceleration of 23.5 m/s2 as the fan comes up to speed. What is the angular acceleration α of the blades?A vinyl record on a turntable rotates at 33 rev/min. (a) What is its angular speed in radians per second? What is the linear speed of a point on the record (b) 15 cm and (c) 7.4 cm from the turntable axis?
- At t = 0 it is observed that a rotating object has an angular velocity of 3 rad/s. The object also has an angular acceleration of 2 rad/s/s. By what angle does the object turn in 4 seconds?A flywheel with a diameter of 1.27 m is rotating at an angular speed of 272 rev/min. (a)What is the angular speed of the flywheel in radians per second? (b)What is the linear speed of a point on the rim of the flywheel? (c)What constant angular acceleration (in revolutions per minute-squared) will increase the wheel's angular speed to 793 rev/min in 98.7 s? (d)How many revolutions does the wheel make during that 98.7 s? [Answer:(a)28.5 rad/s; (b)18.1 m/s; (c)317 rev/min2; (d)876 rev]. Show workStarting from rest at t = 0, a wheel undergoes a constant acceleration from t = 0 to t = 10 s. When t = 3.0 s, the angular velocity of the wheel is 6.0 rad/s. Through what angle does the wheel rotate from t = 0 to t = 20 s.
- A wind turbine is rotating counterclockwise at 0.78 rev/s and slows to a stop in 21 s. Its blades are 27 m in length. (a) What is the angular acceleration of the turbine (in rad/s)? (Indicate the direction with the sign of your answer.) |rad/s2 (b) What is the centripetal acceleration (in m/s2) of the tip of the blades at t = 0? (Enter the magnitude. Round your answer to at least two decimal places.) m/s? (c) What is the magnitude (in m/s) of the total linear acceleration of the tip of the blades at t = 0? (Round your answer to at least two decimal places.) m/s2 What is the angle that this total linear acceleration vector makes with the centripetal acceleration vector? (Enter the magnitude of the smallest such angle in degrees.)A solid sphere is released from the top of a ramp that is at a height h, = 1.85 m. It rolls down the ramp without slipping. The bottom of the ramp is at a height of h, = 1.48 m above the floor. The edge of the ramp is a short horizontal section from which the ball leaves to land on the floor. The diameter of the ball is 0.12 m. (a) Through what horizontal distance d, in meters, does the ball travel before landing? 1.25 m (b) How many revolutions does the ball make during its fall? 3.0 What is the angular speed of the ball at the moment it leaves the ramp? How is angular speed defined in terms of the time and the angle? revA solid cylinder of mass 4.6 kg and radius 0.6 m starts from rest at the top of a ramp, inclined 21°, and rolls to the bottom without slipping. (For a cylinder I = 0.5MR2) The upper end of the ramp is 7 m higher than the lower end. Find the linear velocity of the cylinder when it reaches the bottom of the ramp? (g = 9.8 m/s2)
- A wheel with a radius 0.38 rolls across the level ground, initially moving forward with a speed of 17.3 m/s. After 30 revolutions, the wheel has a speed of 8.43. What must it's constant angular acceleration be?A flywheel with a diameter of 0.679 m is rotating at an angular speed of 221 rev/min. (a) What is the angular speed of the flywheel in radians per second? (b) What is the linear speed of a point on the rim of the flywheel?The angular position of a point on a rotating wheel is given by e = 6.57 + 5.41t2 + 4.08t°, where e is in radians and t is in seconds. Att= 0, what are (a) the point's angular position and (b) its angular velocity? (c) What is its angular velocity at t = 8.28 s? (d) Calculate its angular acceleration at t = 2.65 s. (e) Is its angular acceleration constant?