A BASKETBALL (M = 380g; R = 11.5 cm) ROLLS ACROSS A GYM FLOOR AT 1.8 m/s. FIND I

Question

A BASKETBALL (M = 380g; R = 11.5 cm) ROLLS ACROSS A GYM FLOOR AT 1.8 m/s. FIND ITS KINETIC ENERGY. STARTING FROM REST, A BOWLING BALL (m = 7.0 kg)(R = 0.10 m) ROLLS DOWN A RETURN RAMP 80 cm HIGH BACK TOWARD A BOWLER. HOW FAST IS IT MOVING AT THE BOTTOM OF THE RAMP? A PARTICLE (m = 2.6 kg) MOVES IN THE x, y PLANE AT V = 4.0 m/s. theta = 160 degree AND r^rightarrow = (4i + 3j) IN METERS. FIND THE MAGNITUDE AND DIRECTION OF ITS ANGULAR MOMENTUM, R^rightarrow. A TILT- A- WHIRL IS A CARNIVAL RIDE USING A FLAT STEEL DISK (m_D = 800 kg; r_D = 4.0 m), WITH 6 CARS (m_C = 100 kg) BOLTED TO THE EDGE OF THE DISK. EACH CAR HOLDS 3 RIDERS (m_A = 44 kg). THE RIDE COMPLETES ONE ROTATION EVERY 6.0 SECONDS. FIND THE TOTAL ANGULAR MOMENTUM OF THE SYSTEM. HOW FAST IS EACH RIDER MOVING? THE SYSTEM DESCRIBED ABOVE STARTS FROM REST AND REACHES ITS OPERATING ANGULAR VELOCITY AFTER 8.0 SECONDS. FIND THE AVERAGE TORQUE REQUIRED IF THE TORQUE IS APPLIED BY A TANGENTIAL CHAIN DRIVE APPLIED 3.0 m FROM THE ROTATION AXIS, WHAT AVERAGE FORCE IS REQUIRED. HOW MUCH POWER MUST A MOTOR SUPPLY TO MAINTAIN THE MOTION OF THE RIDE. A POTTER'S WHEEL IS A DISK (m = 1.28 kg; R = 15 cm) SPINNING FREELY AT 180 rpm. A STUDENT DROPS A 300 g LUMP OF CLAY ONTO THE WHEEL, 12 cm FROM THE ROTATION AXIS. AT WHAT RATE WILL THE WHEEL SPIN NOW? FIND THE EARTH'S AVERAGE ANGULAR MOMENTUM IN ITS ORBIT.

Explanation / Answer

1) We know that Kinetic energy = 0.5 mv^2 +0.5iw^2

    = 0.5mv^2 +0.5*2/3* mr^2*w^2

= 0.833 mv^2

=0.833*0.38*1.8^2

=1.0255 J aNSWER

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