Rotational motion of belt drive

In summary, the conversation discusses a mechanics problem involving a belt driving a cylindrical wheel. The tension in the belt, T, is related to the effective torque, N, and the velocity of the belt. The solution involves using equations for moment of inertia, velocity, and angular momentum. The summary also notes a mistake in the initial attempt at a solution.
  • #1
kidsmoker
88
0

Homework Statement



I'm just working through a few past mechanics papers and this question came up:

A belt drives the circumference of a cylindrical wheel of radius R and mass M with
no slipping. The tension in the belt is T. Friction in the wheel bearing causes an
effective torque N to act on the wheel.
(i) If the velocity of the belt is constant, what is T in terms of N.
(ii) The bearing is lubricated removing all significant friction and the velocity of
the belt then increases with a uniform acceleration a. Write down T in terms of
M, R, and a.

I'd be greatful if someone could just check through my solutions so that I'm sure doing things correctly.

Homework Equations



I=0.5mR^2 for disc
v=wr
L=I(dw/dt)

The Attempt at a Solution



(i) T=N .

(ii) v=wR implies dw/dt = a/R .

Therefore TR = 0.5MR^2 * (a/R) ,

and so T = 0.5Ma .

Thanks.
 
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  • #2
One thing I immediately noticed. In [tex]T \neq N[/tex] Why? because this is saying that Force is equal to torque. Surely you know the relationship between torque and force.
 
  • #3
djeitnstine said:
One thing I immediately noticed. In [tex]T \neq N[/tex] Why? because this is saying that Force is equal to torque. Surely you know the relationship between torque and force.


Ah yeah woops! Should be T=N/R ?

Thanks.
 

1. What is rotational motion in belt drives?

Rotational motion in belt drives refers to the circular movement of the belt as it transfers power from one pulley to another. This motion is achieved through the rotation of the pulleys, which are connected by the belt.

2. How does the size of the pulleys affect the rotational motion in belt drives?

The size of the pulleys affects the rotational motion in belt drives because it determines the speed and torque of the rotation. Larger pulleys result in slower rotation but higher torque, while smaller pulleys result in faster rotation but lower torque.

3. What types of forces are involved in rotational motion in belt drives?

There are two main types of forces involved in rotational motion in belt drives: tension and friction. Tension is the force that pulls the belt tight and allows it to transfer power, while friction is the force that resists the motion of the belt and can cause it to slip.

4. How do you calculate the speed and torque in rotational motion of belt drives?

The speed of the belt can be calculated by dividing the circumference of the pulley by the time it takes to make one full rotation. The torque can be calculated by multiplying the force applied to the belt by the distance from the center of rotation to the point where the force is applied.

5. What are some common applications of rotational motion in belt drives?

Rotational motion in belt drives is commonly used in various machines and systems such as bicycles, cars, and industrial equipment. It is also used in household appliances such as washing machines and dryers to transfer power from the motor to other moving parts.

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