5. You visit a friend in Grand Rapids, MI, where – in the middle of the night, you decide to construct a pendulum consisting of a heavy metal stick of mass 2 kg and length 1 m with a solid silicon sphere at the end. The mass of the sphere is 0.4 kg, and its radius 20 cm as shown below. If the pendulum is released from rest at an angle of 30°, what is the angular velocity at the lowest point? Axis e 1 m, 2 kg 30° 0.3 kg, 20 cm radius
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- 1 A CC BY UBC Engineering A handyman has left a ladder leaning on a wall which begins to slip. At a given instant, the top of the т and a velocity of vB s2 т ladder has an acceleration aß = 4.4 5.2 both acting downward. S Determine the magnitude of acceleration at the bottom of the ladder, A, and the magnitude of the ladder's angular acceleration at this instant. The length of the ladder is l = 12 m and forms an angle of 0 = 30° with the ground at A. BA dentist's drill starts from rest. After 3.00 s of constant angular acceleration it turns at a rate of 2.80 ✕ 104 rev/min. (a) Find the drill's angular acceleration. rad/s2(b) Determine the angle (in radians) through which the drill rotates during this period. rad54 . A cylinder with rotational inertia 11=2.0kg.m2 rotates clockwise about a vertical axis through its center with angular speed w1=5.0rad/s. A second cylinder with rotational inertia 12=1.0kg·m2 rotates counterclockwise about the same axis with angular speed w2=8.0rad/s. If the cylinders couple so they have the same rotational axis what is the angular speed of the combination? What percentage of the original kinetic energy is lost to friction?
- A child is riding a merry-go-round, which has an angular speed of 2.15 rad/s and an angular acceleration of 0.85 rad/s2 . The child is standing 3.465 m from the center of the merry-go-round. What is the magnitude of the acceleration of the child? A child is riding a merry-go-round, which has an angular speed of 2.15 rad/s and an angular acceleration of 0.85 rad/s2 . The child is standing 3.465 m from the center of the merry-go-round. What is the magnitude of the acceleration of the child? 7.04 m/s2 8.05 m/s2 9.62 m/s2 18.05 m/s2 16.29 m/s2 Next QuestionNext*11. The sun appears to move across the sky, because the earth spins on its axis. To a person standing on the eartlı, tlhe sun subtends an angle of 0 = 9.28 x 10-³ rad (see Conceptual Example 2). How much time (in seconds) does it take for the sun lo move a distance equal to its own diameter?1. A horizontal platform in the shape of a disk rotates in the horizontal plane about a frictionless vertical axle. The platform has a mass of 150 kg and a radius 2.5m. A student whose mass is 30 kg walks slowly from the rim of the disk towards its center.lf the angular speed is 1.5 rad/s when the boy is at the rim (a)What is the angular speed when the student has reached a point 1.0 m from the center?
- 3. A telephone pole has been knocked over by the wind so that it makes an angle of 0 with the vertical. The wind has stopped blowing and the pole is to be cut down as shown. nail L cut Once the cut is across most of the thickness of the pole, the pole begins to tip over. As the pole tips, the bottom of the pole stays attached to the base by the remaining part of the pole that was not cut (but the torque from the base on the tipping pole is negligible). There is a nail (of negligible mass) on the pole located a distance x. The length of the pole from the cut to the top is L. Remember that the moment of inertia of a stick of mass m and length L about its end is mL?.1. A carousel is initially at rest. At t = 0 it is given an angular acceleration of 0.088 rad/s^2, which increases its angular velocity for 15 secs. At t = 15, determine the linear velocity, in m/s, of a child riding the carousel located 1.37 m. from the center. Round off to two decimal places.A figure skater performs a twisting jump. She rotates around her longitudinal axis 2 times in 0.65 s. What was her angular displacement in radians? A 4 В D 720 E 2m
- A dentist's drill starts from rest. After 4.50 s of constant angular acceleration it turns at a rate of 2.00 ✕ 104 rev/min. (a) Find the drill's angular acceleration. rad/s2(b) Determine the angle (in radians) through which the drill rotates during this period. rad2.5 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)1. The blades of a fan running at low speed turn at 300 rpm. When the fan is switched to high speed, the rotation rate increases uniformly to 430 rpm in 5.30 s. What is the magnitude of the angular acceleration of the blades? rad/s2 f60 ssi f60 0 ssro0