A simple pendulum is made of a 50 cm-string and a bob of mass m. At t = 0, the pendulum is at its equilibrium position and is given an initial velocity v = 0.1 m/s. The maximum angular speed, %3D O'max, is: 0.8 rad/s O 0.1 rad/s O 0.4 rad/s O 0.2 rad/s

3. A uniform disk of mass M and radius R compressed a spring (with spring constant k) a distance of xo from equilibrium. The spring is released and the disk begins to roll smoothly (there is no friction between the spring and the disk) up a ramp, as seen in (I) of the figure below. (1) M, R (II) Max Height, H ++ k ¦¦M,R H }/ (a) What is the speed of the disk after it is released from the spring? (b) What is the maximum height, H, reached by the disk? Imagine now, as seen in (II), that the disk is reset to its initial position and the ramp is replaced with one that abruptly ends after a vertical height of H/2, where H is what you found in (b), and guides any rolling on it straight up. (c) The disk is once again released from the spring. What is the new maximum height it reaches (in mid-air)?

7. A 5.00-kg solid ball of radius 0.250 meters is pressed back against a spring having a spring constant of 1625 N/m, compressing the spring by 20.0 cm. The solid ball is released, and the object rolls 1.00 meter on a frictionless horizontal surface (without slipping) and then rolls up a rough 3.00 meter long incline plane (with an angle of 10.0 degrees to the horizontal). The ball eventually comes to rest at the top of the incline plane. When the ball rolls down the incline plane and compresses the spring, how much will the ball compress the spring? 3.00 m 1.00 m

When a 3 kg mass is hung on a vertical spring, it extends the spring by 3.00 m. What is the angular velocity ω (in rads/s) of the mass when it oscillates back and forth on this spring?

The 11 kg disk has an angular velocity of w = 20 rad/s. (Figure 1) Figure 400 mm 500 mm 200 mm- A B ⒸO 500 mm с P (N) 5 2 1 of 1 -t(s) Part A If the brake ABC is applied such that the magnitude of force P varies with time as shown, determine the time needed to stop the disk. The coefficient of kinetic friction at B is μ = 0.4. Neglect the thickness of the brake. Express your answer to three significant figures and include the appropriate units. t = 0 Submit Value μA Provide Feedback Request Answer Units ? Next >

A solid cylinder of mass 1.1 kg and radius. 19 cm is yoked to a spring as shown. To be pre- cise, the axle of the cylinder is attached to a horizontal spring of force constant 719.7 N/m. The cylinder rolls back and forth on a hori- zontal base without slipping. For simplicity, assume that the spring, the axle and the yoke which connects them have negligible masses compared to the cylinder itself. 719.7 N/m momo 1.1 kg What is the angular frequency of the cylin- der rolling back and forth around the equlib- rium position? Answer in units of s-¹.

A coin having a mass of m = 12 g, a thickness of h = 0.17 cm, and a radius of r = 1.5 cm has a small hole drilled through it so that it can be suspended from a thin wire and worn as an earring or pendant. The hole is at a distance of 7/8 r from the center of the coin as shown above. When suspended from this hole, the coin is a physical pendulum that swings back and forth with this hole as its axis of rotation. Assuming that the hole does not appreciably change the center of mass of the coin, determine the period of this physical pendulum.