PhysicsLAB: Rotational Kinetic Energy

Refer to the following information for the next three questions.

A block and a hoop are both given an initial velocity of v_o = 5 m/sec at the bases of their identical inclines.

To what height, H, will the block slide up its incline if the incline is tilted at an angle of q = 53º?

To what height, h, will the hoop roll up its incline if the incline is also tilted at an angle of q = 53º?

What is the ratio of h/H?

Refer to the following information for the next two questions.

A thin hoop of mass, M, is released from rest and rolls down an incline of length L.

If M = 1 kg, L = 1 meter, and q = 37º, how fast will the hoop be traveling when it reaches the base of the incline?

After the hoop reaches the bottom of the incline it then rolls across a table flying off its edge and subsequently striking the ground. If the table is 80-cm tall, how far from the base of the table will the hoop strike the ground?

Refer to the following information for the next question.

A car of mass, m, rolls from rest down an incline of height, h.

If each cylindrical wheel has an additional mass of (¼)m and radius, r, develop an expression for the car's translational velocity when it reaches the base of the incline.

Refer to the following information for the next two questions.

A 6-kg ball is released from rest and rolls down an incline. When it reaches the end of the incline it falls through a height of 3 meters to reach a waiting cart.

What is the ball's velocity when it reaches the base of the incline (before it leaves the table)?

How far from the base of the table should the waiting cart be placed? (HINT: Remember that you have to take components of the ball's velocity to get v_H and v_o so you can complete your H|V chart.)