a circular ring and a disc of same mass ' m' and radius' r' roll down an inclined plane. which one will reach the bottom first? which one will gain higher velocity?
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As the ring's moment of inertia is higher (double) than that of the disc, it will gain less velocity. So the disc travels faster and reaches the bottom first.
disk radius = r mass = m
Moment of inertia = I1 = 1/2 m r²
ring radius = r mass = m
moment of inertia = I2 = m r² = 2 * I1
When they roll down the inclined plane,
the KE = 1/2 m v² + 1/2 I ω²= m g h
Ring: v² = g h
Disc: v² = 4/3 * g h
disk radius = r mass = m
Moment of inertia = I1 = 1/2 m r²
ring radius = r mass = m
moment of inertia = I2 = m r² = 2 * I1
When they roll down the inclined plane,
the KE = 1/2 m v² + 1/2 I ω²= m g h
Ring: v² = g h
Disc: v² = 4/3 * g h
kvnmurty:
click on red heart thanks above
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