A thin cylindrical shell and a solid sphere start from rest and roll without slipping down a 3.0-m-long inclined plane. The cylinder arrives at the bottom of the incline 2.4 s after the sphere does. Determine the angle the incline makes with the horizontal.

A uniform, solid sphere of radius 6.00 cm and mass 4.50 kg starts with a purely translational speed of 2.50 m/s at the top of an inclined plane. The surface of the incline is 2.00 m long, and is tilted at an angle of 32.0∘ with respect to the horizontal. Assuming the sphere rolls without slipping down the incline, calculate the sphere's final translational speed v2 at the bottom of the ramp. v2=   m/s

A uniform solid sphere of radius r is placed on the inside surface of a hemispherical bowl with radius R. The sphere is released from rest at an angle θ to the vertical and rolls without slipping (Fig.). Determine the angular speed of the sphere when it reaches the bottom of the bowl.

A uniform, solid sphere of radius 5.75 cm and mass 4.75 kg starts with a purely translational speed of 1.75 m/s at the top of an inclined plane. The surface of the incline is 2.75 m long, and is tilted at an angle of 27.0∘ with respect to the horizontal. Assuming the sphere rolls without slipping down the incline, calculate the sphere's final translational speed v2 at the bottom of the ramp.

Given:wheel, radius = 16 cmspins with angular speed 75 rev/min.Find tangential velocity of a rock on the edge of the wheel.

50. A projectile is fired up an incline (incline angle ø) with an initial speed v, at an angle 0, with respect to the horizontal (0, ) as shown in Figure P4.50. (a) Show that the projec- tile travels a distance dup the incline, where 2v2 cose, sin(0,- d g cos2 (b) For what value of 0, is d a maximum, and what is that maximum value? Path of the projectile d Figure P4.50

A disk 8.02 cm in radius rotates at a constant rate of 1 260 rev/min about its central axis. (a) Determine its angular speed. rad/s (b) Determine the tangential speed at a point 2.90 cm from its center. m/s (c) Determine the radial acceleration of a point on the rim. magnitude km/s² direction ---Select--- (d) Determine the total distance a point on the rim moves in 2.02 s. m

A bullet is fired at an angle of 60° to the horizontal with an inital velocity of 200m/s. How long is the bulletin the air?