A uniform solid 5.25-kg cylinder is moving up a ramp that is incline at 30° to the horizontal. The initial speed of the cylinder at the bottom of the ramp is 5.00 m/s. Find the maximum distance, d, the cylinder rolls up the ramp (this is not the final height but the length of the incline that the cylinder travels). The moment of Inertia of the cylinder is 1 =½ MR².

If a rigid body has a constant angular acceleration, what is the functional form of the angular velocity In terms of the time variable?

A wheel 2.00 m in diameter lies in a vertical plane and rotates about its central axis with a constant angular acceleration of 4.00 rad/s2. The wheel starts at rest at t = 0, and the radius vector of a certain point P on the rim makes an angle of 57.3 with the horizontal at this time. At t = 2.00 s, find (a) the angular speed of the wheel and, for point P, (b) the tangential speed, (c) the total acceleration, and (d) the angular position.

A gymnast does cartwheels along the floor and then launches herself into the air and executes several flips in a tuck while she is airborne. If her moment of inertia when executing the cartwheels is 13.5kgm2 and her spin rate is 0.5 rev/s, how many revolutions does she do in the air if her moment of inertia in the tuck is 3.4kgm2 and she has 2.0 s to do the flips in the air?

A potter’s wheel of radius 6.8 cm rotateswith a period of 0.52 s. What are (a) the linear speed and (b) the centripetal acceleration of a small lump of clay on the rim of the wheel?(c) How do your answers to parts (a) and (b) change if the periodof rotation is doubled?

Suppose you exert a force of 170 N tangential to the outer edge of a 1.355-m radius 73-kg grindstone (which is a solid disk). What is the angular acceleration of the grindstone αf, in radians per square second, if there is an opposing frictional force of 21 N exerted 0.35 m from the axis?

A mass, m₁ = 8.00 kg, is on a 30.0° incline and it is attached to another mass, m₂ = 10.0 kg, on a 60.0° incline. They are attached with a massless rope over a pulley with a moment of inertia, I, and a radius of R = 0.250 m. There is no friction between the table and the blocks. Ignore air friction, too. We are given that my accelerates up the incline at a = 1.00 m/s². (a) Draw a free-body diagram for both masses and the extended free-body diagram for the pulley. (b) Determine T₁ and T₂. (c) Find the net torque acting on the pulley and (d) its moment of inertia.

a wheel of radius0.20 m is mounted on a frictionlesshorizontal axle. A massless cordis wrapped around the wheel and attachedto a 2.0 kg box that slides ona frictionless surface inclined at angleu = 20 with the horizontal. Thebox accelerates down the surface at 2.0 m/s2. What is the rotationalinertia of the wheel about the axle?

One end of a cord is fixed and asmall 0.500-kg object is attached to theother end, where it swings in a section of avertical circle of radius 2.00 m, as shown inFigure P7.19. When θ = 20.0°, the speed ofthe object is 8.00 m/s. At this instant, find(a) the tension in the string, (b) the tangentialand radial components of acceleration,and (c) the total acceleration. (d) Isyour answer changed if the object is swinging down towardits lowest point instead of swinging up? (e) Explain youranswer to part (d).

A hollow ball of mass Mand radius Ris released from rest at the top of a bumpy track. The starting point is at height Hfrom the bottom and the top of the bump is at height 2H/3from the bottom of the track, as shown in Fig.1.Over the entire course of its motion, the ball rolls without slipping.The acceleration due to gravity has magnitude g and air resistance is negligible. a) Determine the linear speed of the ball at the lowest point on the track. b) Determine which fraction of the mechanical energy of the ball its rotational kinetic energy represents when it reaches the top of the bump. c)Without any calculations, explain whether a block sliding without friction would have a larger, equal or smaller linear speed at the end of the track.