A bob of mass m is suspended from a fixed point with a massless string of length L (i.e., it is a pendulum). You are to investigate the motion in which the string moves in a cone with half-angle θ. a. What tangential speed, v, must the bob have so that it moves in a horizontal circle with the string always making an angle θ from the vertical? b. How long does it take the bob to make one full revolution (one complete trip around the circle)? Express your answer in terms of some or all of the variables m, L, and θ, as well as the free-fall acceleration g.

A roller-coaster car of mass 309 kg (including passengers) travels around a horizontal curve of radius 35.2 m. Its speed is 21.3 m/s. a. What is the magnitude of the total force exerted on the car by the track? answer in N b. What is the direction of the total force exerted on the car by the track? Enter a positive angle if the direction is above horizontal and a negative answer if the direction is below horizontal. answer in degrees c. If the track is frictionless, then what banking angle would ensure that the car does not slide off of the track? (The banking angle is the angle between the direction normal to the track and the vertical.) answer in degrees

6. a. You're driving over the top of a hill with a radius of 15.075 m. How fast would you need to drive over it to just bounce off your seat as you go over the top? Previous submissions: b. How fast would you need to drive over the top for the normal force of the seat pushing up on you to be half your weight? Previous submissions:

An 0.55 kg puck slides in a r =20 cm circle on a frictionless table while attached to a hanging cyliner of mass M = 2.50 kg.  What frequency of rotation keeps the cylinder at rest?  Express your answer in Hz (cycles per second).  Hint:  Solve for speed then convert to frequency.  Use g=10N/kg.

Josh is painting yellow stripes on a road using a paint roller. To roll the paint roller along the road, Josh applies a force of 15 N at an angle of 45° with respect to the road. The mass of the roller is 2.5 kg; and its radius is 4.0 cm. Ignoring the mass of the handle of the roller, what is the magnitude of the tangential acceleration of the roller?   A. 4.2 m/s2   B. 6.0 m/s2   C. 15 m/s2   D. 110 m/s2

A ball having a mass of 5.2 kg is swinging at the end of a cord in a vertical circle of radius 2 m at 5 rev/s. What is the tension in the cord when the ball is a. at the level of the center? b. At the bottom of the vertical circle?

A 280 gg block on a 52.0 cmcm -long string swings in a circle on a horizontal, frictionless table at 80.0 rpm What is the speed of the block? Express your answer with the appropriate units.   What is the tension in the string? Express your answer with the appropriate units.

A weight of mass m1 = 45 kg slides at a constant speed v = 1 m/s in a circle of radius r = 0.65 m on a table as shown on the left. The force of friction is just enough to keep the weight from sliding in towards the center of the table. The weight is attached to a string which hangs down through a hole in the middle of the table; from the other end of the string hangs a cylinder of mass m2 = 17 kg. a) What is the minimum coefficient of friction needed to keep the hanging mass from moving downwards? b) What would be the maximum velocity the weight could have with that same coefficient of friction?

C. The radius of revolution for the microcentrifuge is 8.58 cm and you need to spin at 700g. What RPM should you spin at?

Consider an annular disk rolling down an inclined plane. The annular disk has mass 154 [g], inner radius 8.00 [cm] and outer radius 12.0 [cm]. The inclined plane has a slope that forms an angle of 44.6° with the ground. A.  Suppose that the coefficient of static friction ?s is large enough so that the annular disk rolls without slipping. What is the magnitude of the translation acceleration felt by the annular disk's center of mass in the direction parallel to the slope? B. What is the minimum value that the coefficient of static friction ?s must take so that the annular disk rolls without slipping?